Twilight Zone:
My favorite episode is one that not many people seem to remember. It takes place in a darkened room with a number of people who are dressed in various costumes (i.e. ballerina, soldier, teddy bear, etc.). They don't know how they got there. There are no windows and doors, except for a light high above them. After bickering, they decide to cooperate and try to reach the top. In the end, it turns out they are all toys in a donation barrel for Christmas! What an ironic twist 
Does anyone else remember this episode?
Yep, I remember it. I think it was called "Five Characters in Search of an Exit" or something like that. Very offbeat episode.
My favorite is called "Twenty-Two." It's about the exotic dancer who keeps having dreams of going to the basement of a hospital where the morgue is, an eerie looking nurse bursting through the door and exclaiming, "Room for one more, honey." Features a marvelously ironic ending, but just that creepy nurse and the fact that this was one of the few TZ episodes shot on videotape rather than film (to save money) makes it very disturbing and unusual.
As for OUTER LIMITS, I have vaguer memories of it, and haven't sprung for either of the DVD sets of its two season run. But I remember one episode in particular which takes place, I think, on Mars where the expedition members keep disappearing one by one. No one knows who's doing the killing or what's happening to the bodies. Come to find out there is a monster on Mars that lives beneath the sand, and it had been dragging the doomed settlers under the sand to devour them.