I really enjoy the old television series The Twilight Zone, and to a lesser extent the two television series that it spawned. It has been so long since I saw the movie version that I can't really remember it. I was probably ten or eleven when I saw it.
Here are a few different intros for the original and the 1980s series--I couldn't find the series that aired on UPN in 2002--and the trailer for the film. I trusted the people who uploaded the intros as far as the season it went with, but as I viewed them, each did feel right for the season it posted.
The original The Twilight Zone pilot intro--notice it is absent Rod Serling as narrator.
The intro for season 3, I think.
This is a re-done intro for the later seasons of The Twilight Zone, but it is faithful to the original, except the graphics are sharper.
Twilight Zone: The Movie circa 1983
The second edition of The Twilight Zone circa 1985