Of the many words I have undertaken to flesh out into full-fledged concepts, "joy" is not one of them. So I approach this with some arbitrariness. Most importantly, I recognize a whole category of related emotions, any of which could be identified by a different person as "joy." One person's joy might be "delight"; another's might be "frisson"; still another's might be "rapture." These are just words, though, and without the weight of a treatise behind them--or at least a good definition--people will have a hard time getting onto the same page with each other. I see two different emotions, for instance, between the "joy" of which one is aware while experiencing it, and another kind of "joy" that is impossible to simultaneously experience and be aware of experiencing. And definitely there is a difference between the sort of high-tension "joy" that excites us so much that sitting still is next to impossible, versus the low-tension joy that is so overwhelming we haven't even got any excitement to vent. These are all different emotions. So whatever emotion I pick to take on the mantle of "joy" is going to be, as I said, somewhat arbitrary.
That said, I think Hadriel offers an excellent starting point. Joy is usually an overriding emotion, one that occurs natively in the center of one's emotional color rather than on the periphery of a mood. Joy is powerful, consuming, and very pleasant--either during the episode, thereafter, or both. Joy is a hard emotion to catch; in the popular sense of the word, joy is too passionate for us to continue to experience for a long period of time. It is a bright, thrilling, flamboyant emotion that allows us to dispense with some deep inhibitions. Joy is more expressive than contemplative. Joy is hard to identify with in other people, unless we are able to experience some bit of it ourselves. It is especially hard to depict in literature and film--although good writers and actors have often made it look a cinch.
In my mind, as I sift through a number of emotions, I think it best for me to leave it at that rather than define joy explicitly. Since I don't have a philosophical concept of joy yet, I don't want to play that card as though there were any weight behind it. Both Hadriel and Radical Dreamer have given good representations of two different emotions that I think would qualify for "joy,' depending on how you look at it. As for me, I find this a useful thread because I never before consciously realized just how large the "happy" branch of the emotional family tree is. There is a lot of exploring to be done here.