I like only the original series.
My favourite ST moment was the one in which Spock was alone on a shuttlecraft and needed to be rescued by the Enterprise. But the rescue would jeopardise the Enterprise and delay its mission, so Spock entered into a discourse, explaining why abandoning him to his fate was the "logical" thing to do. Dr. McCoy was on the bridge at the time, along with Kirk, Sulu etc. After Spock had said his piece, McCoy bellowed "Shuddup, Spock! We're rescuing you!". To which Spock replied "Why thank you, Captain McCoy!" - ROFL! for me, the funniest ever ST moment.