Definitions 
 

Empathy is most often defined by the metaphors of 'standing in someone else's shoes' or 'seeing through someone else's eyes'. Scholars who study empathy have come up with at least 8 ways that the word is used.

8 Definitions of Empathy
(from The Social Neuroscience of Empathy, These Things Called Empathy, Daniel Batson)
"The term empathy is currently applied to more than a half-dozen phenomena."

1. Knowing another persons internal state, Including thoughts and feelings
2. Adopting the posture or matching the neural responses of an observed other
3. Coming to feel as another person feels
4. Intuiting or projecting oneself into another's situation
5. Imagining how another is thinking and feeling
6. Imagining how one would think and feel in the other's place
7. Feeling distress at witnessing another person's suffering
8. Feeling for another person who is suffering  (empathic concern)  An other-oriented emotional response elicited by and congruent with the perceived welfare of someone in need. Includes feeling sympathy, compassion, tenderness and the like (i.e. feeling for the other, and not feeling as the other)

A definition by Frans De Waal author of 'The Age of Empathy' 
What exactly is empathy?
Empathy: The capacity to

a) be affected by and share the emotional state of another,

b) assess the reasons for the other’s state, and

c) identify with the other, adopting his or her perspective. This definition extends beyond what exists in many animals, but I employ the term “empathy” even if only the first criterion is met as I believe all of these elements are evolutionarily connected....more.

Compassion & Empathy  at Greater Good Science Center Wiki
"Strict dictionary definitions have a hard time separating the feelings of empathy, sympathy, compassion, and pity. Often these words are used to define each other. However research on the concepts has begun to pull them apart.

• Empathy is considered a mirroring or vicarious experience of another's emotions, whether they be sorrow or joy. 
• Sympathy  on the other hand, is a feeling of sorrow associated specifically with the suffering or need of another. These are examples of fellow-feeling, and they require a certain degree of equality in situation or circumstances. 
• Pity  which regards its object not only as suffering, but weak, and hence as inferior. 
• Compassion is much like sympathy in that it stems from the suffering of another, but it also includes the need or desire to alleviate suffering" (Eisenberg, 2002).

Carl Rogers: Empathic: An Unappreciated Way Of Being

EARLY DEFINITIONS: The state of empathy, or being empathic, is to perceive the internal frame of reference of another with accuracy and with the emotional components and meanings which pertain thereto as if one were the person, but without ever losing the “as if” condition. Thus it means to sense the hurt or the pleasure of another as he senses it and to perceive the causes thereof as he perceives them, but without ever losing the recognition that it is as if I were hurt or pleased and so forth. If this “as if” quality is lost, then the state is one of identification. (pp. 210—211. See also Rogers, 1957.)
 

A CURRENT DEFINITION: With this conceptual background, let me attempt a description of empathy that would seem satisfactory to me today. I would no longer be terming it a “state of empathy,” because I believe it to be a process, rather than a state. Perhaps I can capture that quality.
 

An empathic way of being with another person has several facets. It means entering the private perceptual world of the other and becoming thoroughly at home in it. It involves being sensitive, moment by moment, to the changing felt meanings which flow in this other person, to the fear or rage or tenderness or confusion or whatever that he or she is experiencing. It means temporarily living in the other’s life, moving about in it delicately without making judgements; it means sensing meanings of which he or she is scarcely aware, but not trying to uncover totally unconscious feelings, since this would he too threatening. It includes communicating your sensings of the person’s world as you look with fresh and unfrightened eyes at elements of which he or she is fearful. It means frequently checking with the person as to the accuracy of your sensings, and being guided by the responses you receive. You are a confident companion to the person in his or her inner world. By pointing to the possible meanings in the flow of another person’s experiencing, you help the other to focus on this useful type of referent, to experience the meanings more fully, and to move forward in the experiencing.
 

To be with another in this way means that for the time being, you lay aside your own views and values in order to enter another’s world without prejudice. In some sense it means that you lay aside your self; this can only be done by persons who are secure enough in themselves that they know they will not get lost in what may turn out to be the strange or bizarre world of the other, and that they can comfortably return to their own world when they wish.

Perhaps this description makes clear that being empathic is a complex, demanding, and strong - yet also a subtle and gentle - way of being.

Question: "What is the Definition for Empathy?"

Marshall Rosenberg: "Empathy, I would say is presence. Pure presence to what is alive in a person at this moment, bringing nothing in from the past. The more you know a person, the harder empathy is. The more you have studied psychology, the harder empathy really is. Because you can bring no thinking in from the past. If you surf, you'd be better at empathy because you will have built into your body what it is about. Being present and getting in with the energy that is coming through you in the present. It is not a mental understanding."

Question: "Is it speaking from the heart?"

Rosenberg: "What? Empathy? In empathy, you don't speak at all. You speak with the eyes. You speak with the body. If you say any words at all, it's because you are not sure you are with the person. So you may say some words. But the words are not empathy. Empathy is when the other person feels the connection to with what's alive in you."

At OneLook.com

Wikipedia.org
Empathy is the capacity to recognize or understand another's state of mind or emotion. It is often characterized as the ability to "put oneself into another's shoes", or to in some way experience the outlook or emotions of another being within oneself. Empathy does not necessarily imply compassion, or empathic concern because this capacity can be present in context of compassionate or cruel behavior... (extensive article)

Vocabulary.com
an understanding of and identification with the emotions of another person
Both empathy and the related word sympathy come from the Greek word pathos, "emotion." To say you empathize with someone is to say you feel their pain or emotions. If you are empathetic, you "put yourself in someone's place" and try to understand exactly how they feel. As Atticus Finch said in To Kill a Mocking Bird, "You don't truly know a man unless you have walked a mile in his shoes." That is empathy.
- Because she was once destitute herself, she has great empathy for the homeless. (compassion, sympathy)
- As a nurse, she does more than offer medical care; she provides empathy and comfort as well. (understanding, compassion)
- Experiencing the death of a close friend has allowed me to be more empathetic with other grieving people. (understanding) adjective
- He seems like a cold and heartless man; he has no empathy for others. (compassion, sympathy)

Encarta.msn.com
1. understanding of another's feelings: the ability to identify with and understand somebody else's feelings or difficulties
2. attribution of feelings to an object: the transfer of somebody's own feelings and emotions to an object such as a painting

Merriam-webster.com
Greek empatheia, literally, passion, from empathēs emotional, from em- + pathos feelings, emotion - more at pathos  Date:1850
1: the imaginative projection of a subjective state into an object so that the object appears to be infused with it
2: the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings, thoughts, and experience of another of either the past or present without having the feelings, thoughts, and experience fully communicated in an objectively explicit manner ; also : the capacity for this

Wiktionary.org
Etymology: A twentieth-century borrowing of Ancient Greek ἐμπάθεια (empatheia), literally passion (formed from εν- en-, in, at + πάθος pathos feeling), coined by Rudolf Lotze to translate German Einfühlung. The modern Greek word εμπάθεια has an opposite meaning denoting strong negative feelings and prejudice against someone.
Empathy
1. the intellectual identification of the thoughts, feelings, or state of another person
2. capacity to understand another person's point of view or the result of such understanding

Britannica.com
the ability to imagine oneself in another’s place and understand the other’s feelings, desires, ideas, and actions. It is a term coined in the early 20th century, equivalent to the German Einfühlung and modeled on “sympathy.” The term is used with special (but not exclusive) reference to aesthetic experience. The most obvious example, perhaps, is that of the actor or singer who genuinely feels the part he is performing. With other works of art, a spectator may, by a kind of introjection, feel himself involved in what he observes or contemplates. The use of empathy is an important part of the counseling technique developed by the American psychologist Carl Rogers.

Stanford Encyclopedia of Philosophy

Infoplease.com
1. the intellectual identification with or vicarious experiencing of the feelings, thoughts, or attitudes of another.
2. the imaginative ascribing to an object, as a natural object or work of art, feelings or attitudes present in oneself: By means of empathy, a great painting becomes a mirror of the self.
Origin:  1900–05; < Gk empátheia affection, equiv. to em- em- ² + path- (base of páschein to suffer) + -eia -ia; present meaning translates German - Einfühlung

Encarta.msn.com
1. understanding of another's feelings: the ability to identify with and understand somebody else's feelings or difficulties
2. attribution of feelings to an object: the transfer of somebody's own feelings and emotions to an object such as a painting

Bartleby.com
Identifying oneself completely with an object or person, sometimes even to the point of responding physically, as when, watching a baseball player swing at a pitch, one feels one’s own muscles flex.

Allwords.com
1. the intellectual identification of the thoughts, feelings, or state of another person
2. capacity to understand another person's point of view or the result of such understanding
Etymology: A twentieth-century borrowing of Ancient Greek á (empatheia), literally "passion" (formed from - en-, "in, at" + pathos "feeling"), coined by w:Rudolf Lotze, Rudolf Lotze to translate German Einfíhlung. The modern Greek word has an opposite meaning denoting strong negative feelings and prejudice against someone.

concord, accord, harmony, symphony, agreement, sympathy, union, unison, unity, unanimity, league, friendship, alliance, understanding, conciliation;
antonym: Discord

Etymonline.com
1903, translation of Ger. Einfühlung (from ein "in" + Fühlung "feeling"), coined 1858 by Ger. philosopher Rudolf Lotze (1817-81) from Gk. empatheia "passion," from en- "in" + pathos "feeling" (see pathos). A term from a theory of art appreciation. Empathize (v.) was coined 1924; empathic (adj.) is from 1909.

EMPATHIEA-"Empathy literally means the power of understanding things outside ourselves after the Greek empatheia, but has come to imply a reliance on inner feeling"

 feeling into another individuals emotional state (einfuhlung)" Lipps 1903 -
"empathy involves resonating with other peoples unconscious affect" - feeling vibrations?

On Empathy: By: Dr. Sam Vaknin - The Encyclopaedia Britannica (1999 edition) defines empathy as:
"The ability to imagine oneself in an other's place and understand the other's feelings, desires, ideas, and actions. It is a term coined in the early 20th century, equivalent to the German Einfühlung and modeled on "sympathy." The term is used with special (but not exclusive) reference to aesthetic experience. The most obvious example, perhaps, is that of the actor or singer who genuinely feels the part he is performing. With other works of art, a spectator may, by a kind of introjection, feel himself involved in what he observes or contemplates. The use of empathy is an important part of the counseling technique developed by the American psychologist Carl Rogers."

Carl  Rodgers - THE PERSON-CENTERED APPROACH

The first quality is empathy. Many people believe that this is the single quality which is most important in all forms of therapeutic listening. It means getting inside the world of the person who comes for therapy (usually called the client, though some people not in this group prefer other words such as patient or consulter) so that that person feels accepted and understood. Two things are important about this:
 (1) that the empathy be accurate, and
(2) that the empathy be made known to the client.
Both of these are learnable skills, and they do make a huge difference to the relationship between client and counselor or therapist.

The second quality is genuineness. If empathy is about listening to the client, genuineness is about listening to myself - really tuning in to myself and being aware of all that is going on inside myself. It means being open to my own experience, not shutting off any of it. And again it means letting this out in such a way that the client can get the benefit of it. Genuineness is harder than empathy because it implies a lot of self-knowledge, which can really only be obtained by going through one's own therapy in quite a full and deep way. It is only a fully-functioning person (Rogers' word for the person who has completed at least the major part of their therapy) who can be totally genuine.

The third quality is non-possessive warmth. It means that the client can feel received in a human way, which is not threatening. In such an atmosphere trust can develop, and the person can feel able to open up to their own experiences and their own feelings.
" Empathy is respectful understanding of what others are experiencing. " Marshall B. Rosenberg

Wikipedia: Theorists and their definitions

A motivation oriented towards the other.   Daniel Batson

The capacity to know emotionally what another is experiencing from within the frame of reference of that other person, the capacity to sample the feelings of another or to put oneself in another’s shoes.    D. M. Berger

A sense of similarity in feelings experienced by the self and the other, without confusion between the two individuals.  Jean Decety

An affective response that stems from the apprehension or comprehension of another’s emotional state or condition, and that is similar to what the other person is feeling or would be expected to feel.   Nancy Eisenberg

 To empathize means to share, to experience the feelings of another person.   R. R. Greenson

 The ability to put oneself into the mental shoes of another person to understand her emotions and feelings. Alvin Goldman

An affective response more appropriate to another's situation than one's own. Martin Hoffman

A complex form of psychological inference in which observation, memory, knowledge, and reasoning are combined to yield insights into the thoughts and feelings of others.  William Ickes

Empathy is the capacity to think and feel oneself into the inner life of another person.  Heinz Kohut

To perceive the internal frame of reference of another with accuracy and with the emotional components and meanings which pertain thereto as if one were the person, but without ever losing the "as if" condition. Thus, it means to sense the hurt or the pleasure of another as he senses it and to perceive the causes thereof as he perceives them, but without ever losing the recognition that it is as if I were hurt or pleased and so forth.  Carl Rogers

Empathy involves the inner experience of sharing in and comprehending the momentary psychological state of another person.  Roy Schafer

"We recognize others as empathic when we feel that they have accurately acted on or somehow acknowledged in stated or unstated fashion our values or motivations, our knowledge, and our skills or competence, but especially as they appear to recognize the significance of our actions in a manner that we can tolerate their being recognized." Wynn Schwartz

Empathy is the experience of foreign consciousness in general.  Edith Stein

In popular usage the idea refers to the emotional resonance between two people, when, like strings tuned to the same frequency, each responds in perfect sympathy to the other and each reinforces the responses of the other. A good example of this occurs in the statement: “Aleatoric concert music, like jazz, demands a strong empathy between performer and listener” (Houkom, p. 10).

Empathy is about spontaneously and naturally tuning into the other person's thoughts and feelings, whatever these might be [...]There are two major elements to empathy. The first is the cognitive component: Understanding the others feelings and the ability to take their perspective [...] the second element to empathy is the affective component. This is an observers appropriate emotional response to another person's emotional state.  Simon Baron-Cohen (2003):

"[Empathy] is what happens to us when we leave our own bodies...and find ourselves either momentarily or for a longer period of time in the mind of the other. We observe reality through her eyes, feel her emotions, share in her pain.." Khen Lampert (2005):