I wouldn’t dream of spoiling it! I can still remember seeing it on first broadcast aged 8! In fact now I come to think about it, the end of series 3 was pretty memorable as well.
I do recall that most of S4 was a bit underwhelming, but they certainly go out on a high.
Which reminds me, I wonder what happened to the remake that was announced a couple of years ago. It was supposedly being done by Sky, who co-financed the new BSG.
For me it’s always Angel. The last moment with Wesley & Illyria, and how Spike chose to spend his evening (calling back to longtime Buffy fans such as myself), and the final perfect moment. I can’t believe they wrote comics set after that - it was such a fitting way to go out for those characters!
DS9 worked really well for me - the moment where Martok drinks to their glorious victory & Ross & Sisko look at the destruction all around them & can’t toast with him was priceless. And the characters all got to move on in ways that suited them all so well … I loved it.
And going back even farther - the most Final finale I’ve seen was Forever Knight. The last season was terrible (I especially hated that new partner - her last words were the only interesting thing she ever said), but then in the last episode they kill off half the cast. There’s finality for you! 
These are the ones that came to my mind also. Both choked me up and made me smile at the same time. Very satisfying. I loved that J.Michael Straczynski appeared in the pilot “The Gathering”, and that he played the workman who was the last guy to leave the B5, and turned out the lights. Awesome, awesome moment. Still affects me.
Where was he in The Gathering?
Glad somebody bumped this, because I missed it the first time through somehow.
Lots of great ones have been mentioned so far, so I’ll throw out some more:
Somebody said The West Wing season 2, finale. Best of the series? Maybe, but I submit the end of Season 3, “Posse Comitatus”.
Quick background for the uninformed- Martin Sheen’s Character is the President, and is running for re-election. The other guy is his challenger, and they are a couple months out from the election.
Other Season Finales that have not been mentioned:
Babylon 5, Season 3: Za’ha’dum. You know how when things get really epic at the end of a show or movie, they start cutting between different characters without any transition or set up or anything? They start that 30 minutes into this episode!
SG1, Season 6: Full Circle (ok, somebody mentioned this, but its worth mentioning again). This was originally intended as a series finale, and its one of my favorite SG1 eps. The destruction of the the Pyrimd is one of the great effects moments of the series as well.
Scrubs, Season 4: My Changing Ways. Elliot leaves the hospital, JD finally moves out of Turk and Carla’s apartment, and realizes change is inevitable. Don’t know why, this one has always stuck out for me.
Yeah. I really really liked that one.
MASH IMHO, was the Best Ever…and maybe better then that.
" Doctor, I’ve seen the captain feverish, sick, drunk, delirious, terrified, overjoyed, boiling mad… but up to now, I have never seen him red-faced with hysteria. "
I love it.
I also really liked Barney Miller’s series finale.
For me, Scrubs Season 8 finale, the pictures of JD and Elliot’s future shining on JD’s face with the music playing turns me into a sobbing wreck every time I watch it.
After that, Black Adder Season 4 and the finale of Angel were terrific and brought both series to a proper close.
Let’s see, from memory, in one of the early scenes, he’s one of two businessmen who are talking to a telepath.
I remember that! It was an awesome way to end the show.
I can’t find any reference to JMS making a cameo in ‘The Gathering’. I’ll have to go back and watch it.
Ok, start watching - at about 19 mins into it, you’ll see Leta sitting at a table with two men. The guy facing the camera is JMS. He has computer at the table.