CBS is now offering some older series streaming on their website, including all three seasons of the original Star Trek. Well worth checking out. They also have Twilight Zone episodes, though only two seasons of those.
I recommend City on the Edge of Forever from the first season and The Doomsday Machine from the second season. The latter has a great "impending disaster" musical theme to it.
The only downside is that you can't zoom to full screen, which is a failing of the CBS video player. I like to watch Big Brother on their website, so this thing's been bugging me a while, but it's vastly outweighed by the joy of FREE TREK!