I’m going to second the Angel finale. I thought the show still had one more good season in it, but the ending left me satisfied and had a lot of great moments.
I’m going to say Wonderfalls.
Not the last episode aired on broadcast TV, but the last one filmed, which you can see on the DVD. For a one-season show cancelled before it even ran its whole season, it managed to wrap things up in a very satisfying package at the end of that last episode.
It’s not as bad if you cut off the last 5 minutes. 
That being said, Knauff had the entire storyline of the series planned for one season. HBO said they liked it, but wanted to run for five, so he’d have to stretch it. They then cancelled him after two.
Knauff hasn’t posted exactly where he wanted the story to go (I think he’s still searching for a new venue for it), but he did post a lot of the underlying ‘mythology’ of the world, which I found very satisfying.
The OP didn’t ask for SEASON finales. But my favorite surprising-but-clearly-planned-from-the-beginning-and-totally-satisfying resolution to a season-long story arc is found in season 1 of Veronica Mars.
HBO did cut Carnivale’s legs out from under itself. The “finale” was never meant to be a series finale. Right now I have my fingers crossed for Lost and How I Met Your Mother.
I loved Quantum Leap but lost track of it in its final season (freshman year at college) and I’ve yet to see the finale but I know the story very well. It probably would have reduced me to tears…
On the few occasions that I have outlined it for someone, just retelling the story has never failed to mist me up.
The Firefly movie, though obviously they semi-cheated by finishing it up in a movie rather then a series finale. They were probably helped by the short run of the series as well, as they didn’t have a million random plot threads to have to try and cram into some overarching explanation (unlike X-Files or Lost), so they could bring things to a pretty tight conclusion.
The similar Cowboy Beebop keeps the back story of its protagonist fairly mysterious until the excellent finale.
I’ll have to try Babylon 5 again, I tried to watch it once and couldn’t make it through season 1.
I thought of this, too. It was ABSOLUTELY INFURIATING at the time, but in hindsight it’s reasonably clever & very memorable.
Not as good as just getting Sam home, though.
Well, try not to become “season one roadkill” by B5. It’s a very common problem with people who try to get into B5. S1 is very weak overall. Seasons 2-4 are far better.
This might have been it for me if not for the words at the end. I even liked the Al’s exwives are now his daughters thing. But “Sam never got home” is blasphemy. They should have had Sam show up for his “sabbatical” and embrace his wife, maybe be introduced to Al’s daughters, and then have the bartender show up and say “Sam, it’s time…” and have Sam start leaping again.
“All Good Things” from ST:TNG would be perfect if it didn’t have that one giant temporal inconsistency. And it would have been so easy to fix, too.
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How would you have fixed it?
This is my choice. It left some room open for the whole Mal/Inara romance but it tied up the whole River mytharc and Reaver stuff nicely while just being a general kick ass movie to boot.
If we’re allowed to broaden it to all types of series I would have to choose Six Feet Under as being the perfect series finale.
If memory serves, the problem is two-fold: first, they show up in the future in Beverly’s ship, not the Enterprise, and second the anomaly isn’t there until they start probing, despite the fact that it expands backward through time. Getting them onto the Enterprise before they get there is simple enough though probably requires the most re-writing. The other part is even simpler to fix: they show up, the anomaly is there but tiny, and they decide to probe it. The instant the probe beam touches it, it winks out of existence. Easy peasy.
And then how does Picard collapse it in all three time frames? 
And I was totally disappointed by the movie; in the series, the River character was balanced out by her imbalance: while she had scary abilities, their “activation” had driven her nuts; so, although she could outcompete anyone, she couldn’t do that for any longer period of time. Sometimes she was supergirl, sometimes almost a vegetable.
But the movie turned her into yet another one of Whedon’s uberpowered slayer girls who manage to eat the cake and keep it. Gah.
Angel would have had a perfect ending if there was no season 5, and Buffy should have ended there; but I have to admit, that this has a lot to do with my dislike of Spike’s story line (in both series) and its muddying consequences for the established myths.
I think “Rome” ended in a way that answered all relevant questions and completed the major character arcs quite well. Besides, Max Pirkis’ portrayal of young Octavian was, imo, brilliant and I wished, Dekker could characterize John Connor as someone half as capable.
Different problem. 