Hard to pick just one. Any with P McGoohan .
I think it's very hard to beat Negative Reaction.
Although I'm kind of biased about the first two seasons. One particular one is Greenhouse Jungle.
Hard to narrow it down to ONE episode so I'm going to list FOUR, with different reasons:
Columbo Goes to College - because it's the first episode I ever saw, when it first ran on ABC TV. After that I was hooked, and recorded the A&E older episodes on VHS, in addition to watching all of the subsequent ABC episodes. I later obtained the DVD boxed sets to finish watching the entire series.
Swan Song - I love the friendly interaction between Peter Falk and Johnny Cash, and Cash's music.
Negative Reaction - My favorite ending. Also clever how the Kodak logo is backwards at the end. Makes you wonder, was the entire episode shown backwards, LOL.
Exercise in Fatality - Two words: Gretchen Corbett.
By Dawns Early Light
Favorites, not necessarily regarded as the best (so hard to pick one, so I had to list several):
"The Conspirators" - Clive Revill's performance has always stood out - singing, acting; always thought the script was especially crisp.
"Troubled Waters" - the whole cruise ship setting was just cool.
"By Dawn's Early Light" - loved the setting again - this time on the campus of The Citadel; Patrick McGoohan's performance
"Murder By the Book" - the first one of the series; still holds up remarkably well. Jack Cassidy at his best and again, the wonderful scenery/locations.
"Death Lends A Hand"
"Murder By The Book"
I agree that it's difficult to pick one. So I'll cheat and pick both an "original" and a "new" episode: Suitable for Framing and Columbo Goes To College.
Suitable for Framing has an arrogant villain, brilliant clues and possibly the best "gotcha" moment of the entire series. True to formula, Dale Kingston's superiority complex causes him to underestimate Lt. Columbo until it's too late. I particularly love the scene where Columbo practically dares Kingston to object to the phone tap. Instead Kingston becomes overconfident, plays the victim as he offers a key to his apartment. I have to paraphrase:
Lt. Columbo: We'll put a tap on your phone. You don't mind do you? After all, they may call you for the ransom.
Dale Kingston (looking taken aback and quickly recovering): Of course not. You can snoop around all you like. You can go through my stuff and you won't find any stolen paintings! Here, take the key to my apartment if you like.
L.C.: Oh no, we don't have to snoop around or anything like that. I wouldn't mind the key of course, you know, to look at some books to learn about art and stuff.
Columbo then takes the key from Kingston who looks completely stunned. Of course this later puts Columbo in position to set up the brilliant "gloved hands" reveal. An absolute classic!
In Columbo Goes To College, the two frat boys, along with the arrogant father, are perhaps the most smug, elitist and condescending fools in the entire run of the show. The murder is ridiculous, but if you get past that, there are some great clues like when Columbo mentions that Rusk was going to Phoenix, or when he plants the gun in the wrong car. Columbo was always a step ahead of these two clowns who mocked him as an inbred.
Honorable mention goes to "Death Hits the Jackpot for the later episodes, but the original run has too many great ones to mention.