I'm sure there have been other great last eps (which we can talk about in the comments), but these are the ones that have stuck in my mind because they're all from recent shows that I am a massive fan of.
Your favourite last ever episode:
Angel (Not Fade Away)
Buffy the Vampire Slayer (Chosen)
Friends (The Last One)
Sex and the City (An American Girl in Paris (part deux))
Six Feet Under (Everyone's Waiting)