From a Facebook thread that raised the question of the difference (if any) between sympathy and empathy. I do enjoy digging down into words...
"Sympathy" is literally "pathos with", "suffering together": "I feel your pain". We use it for positive emotions too, though maybe less often. "1) A feeling of pity or sorrow for the suffering or distress of another; compassion 2) The ability to share the feelings of another." Also, in a more general sense, "3) A mutual relationship between people or things such that they are correspondingly affected by any condition." [ http://en.wiktionary.org/wiki/sympathy ]
"Empathy" is a 20th century term (I did not know that) "coined by Edward Bradford Titchener to translate German Einfühlung", from the Greek for "passion", "in pathos". Wiktionary suggests it is more intellectual: "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." But also, in parapsychology and science fiction, "a paranormal ability to psychically read another person's emotions". [ http://en.wiktionary.org/wiki/empathy ]
I would say that the idea of "theory of mind" [ https://en.wikipedia.org/wiki/Theory_of_mind ] is related to "empathy" in this sense. Via a theory of mind one can identify and understand the feelings of others without necessarily experiencing them.
Einfühlung, though, comes from the 18th century German Romantics: "It is believed that the notion has its source in the philosophy of Johann Gottfried Herder, who thought that while perceiving different natural phenomena one can look for similarities to the human and thus ascribe human feelings to them. Herder endowed Nature with a consciousness which could be penetrated by man thanks to empathy. Empathy leads to a mystical union of the subject and the object, Man and Nature." [ http://argumentwp.vipserv.org/.../10_argument-2-08-Nowak.pdf ]
So the roots of "empathy" are actually more mystical, and I'd say that in some contexts it still carries that connotation... the SF/"New Age" use to mean a sort of telepathy or intuition that senses emotion but not verbal intellectual content, for example.
And I'd say that mystical definition has leaked over into that third definition of sympathy, where people or things are mutually affected.
So. It's complicated.
I'd say that for "I feel your pain" -- or "I feel your joy" -- sort of experiences, "sympathy" is the more accurate term. (Thus, we send a "sympathy card" when to someone who has lost a loved one.) Maybe "empathy" is better used to denote either 1) the general intellectual/psychological capacity to "put yourself in another persons shoes" (the meaning it seems to have in the psychological literature) or 2) the personality trait of being easily moved into identifying with another's feelings and experiences, perhaps even beyond the emotional level to a mystical one.