Best: Angel. The first time I saw it I felt robbed. Later I realized it ended the only way it could. The line, "Let's go to work," in the context in which it is used, is the whole statement of the series. There's no finish line, no trophy, just a job that needs doing. It will never be over for him or his crew, they will fight evil forever.
Best: Buffy. Pulled out all the stops? Check. Beat the enemy at his own game? Check. Descended into the bowels of hell itself and shut that damned mouth once and for all? Check. Epic battle for the fate of the region/world? Check. School is officially out.
Best: Gurren Lagann. The universe -- literally the whole time-space continuum and everything in it -- is against us, but we fight and win anyway. It's hard to get more epic than hurling entire galaxies at your enemy like shuriken.
Worst: Evangelion. Hey, we're all out of money, let's do some clip episodes that have nothing whatsoever to do with anything that's come before!
Worst: Farscape's series finale. Want to kill your main characters? If you must then you must. But you make it mean something. You do not -- that is capital N, capital O, capital T -- you do NOT kill them off arbitrarily, like little bitches, the way nameless extras die during the teaser to show the audience there's a credible threat. (Yes, I am aware of Peacekeeper Wars. THAT is how the series should have ended.)
Worst: Star Trek Voyager series finale. I detest time travel stories and this is the worst. If time travel is possible for humans, we have to assume the Borg, with their vastly superior technology, can do it better. If humans can travel to the future to get ridiculous weapon upgrades, so can the Borg. Any advantage gained would be immediately nullified. For that matter, since time travel is apparently so damn easy, the Borg could just travel backwards a few billion years, zap Earth's primordial soup, and prevent life from ever evolving there. If *I* can think of that, the Borg are definitely smart enough to do it. There is also the complete loss of suspense that comes from dealing with future-Janeway. Obviously if she and the Federation are still around the good guys won the battle. So many problems I could write a book.
EDIT: I see a lot of people picked Lost as the worst ending. I'm working my way through that show right now, haven't seen the end, don't spoil it for me. I read an interview with the writers before the finale was aired. Their comment was it was not their responsibility to answer every question, nor was it to make everyone happy. Their responsibility as writers was to tell an interesting story. If you were unhappy with the way it ended, or that questions went unanswered, that means you were interested. Besides, I would think after watching five and a half seasons you would have understood Lost simply wasn't the kind of show that laid everything out for you in black and white.