Easily one of my favorites is the fifth season TNG ep "The Inner Light" (and how frickin scary is it that I not only know the season but also the title without having to look it up and it has EASILY been 12 years since I last saw it)... Picard thinks he's living the life of Kamin. The things he does while living that alternate life... living the life of a culture long since died... carries with him. The recorder he keeps with him for the rest of the series, for example.

(Ok, I will also admit that fifth season TNG is my absolute favorite anyway, so remembering the episode is really not that big a surprise)