Already mentioned:
Newhart series finale
Fawlty Towers – “The Germans”
Taxi – The yellow light episode. However, the scene that sticks out in my mind is Jim and Tony going at it over Vietnam:
Tony: “The only reason you guys got to stay home, protest and get loaded is because guys like me were over in ‘Nam doin’ your fightin’ for ya! Whaddaya say to that?”
Jim: “Thank you.”
Tony: (chagrined) “You’re welcome.”
Pure gold.
For the rest, wow. There are so many, it’s hard to choose after almost 50 years of TV viewing. I find myself having to go with episodes that play in my head over and over.
TNG – “Encounter at Farpoint”. Like a lot of Trek fans, part of me was thinking, “How can they possibly improve on TOS?” At the end of the episode, I stood up, turned to my friends, and said, “Now, that’s how a military ship is supposed to be run!” Much as I always loved Kirk, Picard became the quintessential starship captain in my eyes that day.
TNG – “Unification”. I could watch this over and over, and not just because of Spock (though that doesn’t hurt). Riker’s encounter with the piano player, the scenes with the head of the surplus depot (“He probably figures that we don’t see a lot of handsome women out this way, and someone like you will get more cooperation…he’s probably right.”), and my personal favorite scene: Data applying the Vulcan pinch to Sela, followed by Spock saying, “Not bad.”
Babylon 5 – So many to choose from, but my vote goes to “Ship of Tears”, the one where Bester’s girlfriend is captured by the Shadows and wires herself to the station. I truly enjoyed seeing Bester’s human side, however briefly.
CSI: – “Jackpot”. Doc Robins receiving the head in the box hooked me right away. The subsequent script represents CSI’s finest hour. The scene with Grissom, the sheriff, and the sheriff’s gay brother almost had me in tears (“I figured you’d tell me when you were ready.”)
Hill Street Blues – Again, a tough choice, but I have to go with Howard Hunter’s first episode after his demotion and appointment as watch sergeant.
“It was hardly my choice to be demoted, Frank…but if I am to be a sergeant, this is the sergeant I would like to be.”
Blackadder – As good as “Goodbyeeee” is, I choose “Bells”, the famous Kate/Bob episode. Edmund’s scene with the doctor is possibly one of the funniest sitcom scenes ever. And I love Lord Flashheart!
Twilight Zone – “The Grave” with Lee Marvin as the bounty hunter. Scared the living bejeebus out of me!