In alphabetical order, here are some of my choices (I'm not picking just one). These are mostly all "comfort food" episodes, ones that I can throw on and guarantee to be entertained.
THE AVENGERS - "Death's Door" This might seem an odd choice to some, but it was an episode that I managed to capture on VHS tape way back in the late '70s/early '80s on a late night run on CBS. As such it was the only episode I could put on when I was in the mood for an AVENGERS episode, thus it became on "old friend". And it's a fun episode to boot.
DICK VAN DYKE - "I'd Rather Be Bald Than Have No Head At All" It's a toss-up between this and the walnut episode. Both have fun dream sequences that I just love. I still use the word "ingrediment" to this day.
THE FUGITIVE - "Nightmare At Northoak" Most will say the finale is the best, and that's a hard choice to deny. But this first-season episode had it all. A dream sequence starts the episode, and its iconic images were used throughout the rest of the series for part of the opening. The menace from Gerard is never stronger, and Kimble has much to overcome in this one.
THE INVADERS - "Beachhead" (pilot) A bunch of my choices are pilots. They often had the biggest budgets, and the premise of the series gets sets up nicely, as is the case here.
LOST IN SPACE - "No Place To Hide" (unaired pilot) This hour of television, without the nonsense of Dr. Smith, was just fabulous. It was so good that it served as the foundation for FOUR series episodes with some clever editing.
LOST - "Man Of Science, Man Of Faith" After an engrossing first season following the plane crash, this first episode of the second season took us to places totally unexpected with the opening of "the hatch." There are other fascinating episodes to be sure, but this one really captured the imagination.
LAND OF THE GIANTS - "The Crash" (pilot) The first and best episode of this series.
M*A*S*H - "Adam's Ribs" Surely one of the funniest M*A*S*H episodes ever.
MANNIX - "The Sound Of Darkness" Our hero is blinded and must rely on friends and his inner strength to survive. None better.
MISSION: IMPOSSIBLE - "The Train" The team uses great "trickonology" to fool a head-of-state wannabee.
THE OUTER LIMITS - "The Forms Of Things Unknown" A more bizarre hour of television you'll never find. Fascinating to watch over and over again as you try to piece together what its all about. Dreamy, surrealistic, with an exceptional music score (later used in THE INVADERS).
THE PRISONER - "The Chimes Of Big Ben" It's hard to pick just one, but this episode has it all, from an iconic Number Two to an escape attempt. Unforgettable.
SECRET AGENT/DANGER MAN - "A Room in The Basement" For some reason this is the most memorable episode of this series for me. The lovely Jane Merrow guest stars.
STAR TREK - "City On The Edge Of Forever" Much has been written of this episode, and it's the one that got me hooked on STAR TREK in the first place. Fabulous stuff.
STAR TREK THE NEXT GENERATION - "The Inner Light" A jaw-droppingly good story that had us wowed from the moment we saw it. Still amazing to this day.
STAR TREK DEEP SPACE NINE - "The Visitor" A for-sure CWWC for me. (That's "Can't Watch Without Crying"). Considered one of the best STAR TREK's of any generation or series.
STAR TREK VOYAGER - "Year Of Hell" Fun sci-fi premise of altering timelines in a two-part story. I also like the one where VOYAGER goes back to 20th century California.
THE TIME TUNNEL - "Rendezvous With Yesterday" (pilot) The best episode of my all-time sentimental favorite series. It sets up the series premise, takes us for a ride on the Titanic, and features some amazing SFX work and tunnel complex shots.
TWILIGHT ZONE - "On Thursday We Leave For Home" Yes, my favorite TZ is an hour-long episode, probably the best of that fourth season, and in my mind one of the best of the series.
VOYAGE TO THE BOTTOM OF THE SEA - "Submarine Sank Here" No monsters running amuck here, this is a tense, gripping story that'll keep you on the edge of your seat. One of the best from a fine first season.
Some of these were mentioned earlier in the thread, some were not. And I'm sure there are others I may think of later and wish I'd have included. But this will do for now.