I am a fan of the original Twilight Zone, and a few years ago, I broke down and bought the entire collection on DVD (Thank you, Amazon). Actually, what happened was, I had a baby and I couldn't watch the marathons held on New Year's anymore. I reasoned that I could have my own marathons this way.
I was also a fan of:
Tales from the Dark Side
Tales from the Crypt
Alfred Hitchcock Presents
The New Twilight Zone
Ray Bradbury Theater. All of these shows* have their own feel, but most of them involve some kind of science fiction and plot twist. Some have aged better than others (I think the Twilight Zone is dated, but in a cool way, unlike some of those series from the '80s). I bought this from Amazon, and get this--the collectable tin with all of the episodes inside is a few dollars less than the same collection without the tin. You get 1571 minutes of show for $16.49 AND a collectable tin. That's just a little over 1 cent per minute! When I compare that to the 3.5 cents per minute I spent on the Twilight Zone, I have to admit--I feel a little cheated.
One of my favorite Ray Bradbury stories was not on his series, but a series called "Wonderworks," which ran on PBS. I thought about it a few months ago and actually found it on YouTube (thank you, Google). I'm embedding the first part, but you should easily be able to find the next two parts of the story there as well.
*In case you were wondering, I never could get into Outer Limits and I've never seen Night Gallery.