I just watched the first five episodes of the original Twilight Zone. Pretty cool. I've seen a few other episodes fairly recently also.
Rod Serling wrote 92 of the 156 episodes himself. He had an interesting imagination and seemed able to see things from a perspective I'm not sure I could access. Many episodes had a twist ending that revealed the "actual" reality the characters inhabited: they are dolls, dead, robots, fictional characters, subjects in a sensory deprivation tank, and so on.
Serling saw very heavy fighting in WW2 and was wounded several times but remained a private after three years because he was kind of a screwup (he would wander off and get lost, for example). The madness of war and arbitrariness of death (he once saw a comedian decapitated on stage by a falling crate) clearly informed his writing.
Many of the episodes don't have much of a point. They seem unable to answer the question "Why did you just tell me that story?" They often seem to be just fucking with the main character, leaving him in a hopeless situation or, strangely, given new hope for a fuller life.
I always sort of assumed that the first couple of episodes would explain the concept of the "twilight zone", but they don't. Apparently the universe just goes a little crazy now and then, and you'd better just hang on and hope you get back to normal reality intact, assuming you even ever existed in normal reality.
On the other hand, the characters are often rather two-dimensional. They often have a lot of trouble realizing or believing what is happening to them. Sometimes this adds to the dreamlike or nightmarish quality of the story, and sometimes it just doesn't ring true.
While One Step Beyond explored ostensibly true paranormal stories and The Outer Limits explored stories about alien invasion, The Twilight Zone focused mostly on regular people trapped in nightmarish circumstances. That—along with better writing overall—is what I think makes it more personal and memorable.
