This is a toughie. A lot of my favorite shows are older and don't have finales. They just end with an ordinary episode. That really leaves me about five shows to choose from: Angel, Buffy the Vampire Slayer, Five Mile Creek, Lost, and Dr. Quinn, Medicine Woman. Hmm.
I do love the finales for Angel and Buffy. They sum up the shows, provide closure for a lot of characters, pull together a lot of plot strings... all things finales should do. I know a lot of people didn't like the open ending of Angel, since it didn't tell you if the last few characters left standing would survive the seemingly insurmountable odds facing them or not. But Angel on a whole was about fighting the good fight, not about winning. So whether they survived or not is kind of moot. (An added plus of the ambiguous ending is that it leaves lots of room for fanfic! The only fully Angel-verse story I've written so far, "Searching," deals with the aftermath of the finale.)
I barely remember the finale for Dr. Quinn. I think it had something to do with Colleen deciding not to go to medical school, but marry Andrew instead. Clearly, as a finale, it didn't impact me enough to be a favorite.
Then there's Lost. I liked the finale. It brought a lot of character-arc closure, my Sawyer ended up happy, and it made the Sideways world make sense. To me, anyway. But I'm not sure I loved it. (Though I do adore that one scene I blogged about earlier.)
So I guess that means that the series finale of Five Mile Creek is my favorite. It's called "America," and in it, Con and Kate finally get married, and they set off for America, promising to send for Sam as soon as they're settled. It's a neat ending, bringing some characters full circle and leaving everyone with a new adventure before them. It's full of joy and hope, but also a little sadness as the happy Five Mile family splits apart somewhat.