You can stream the action, but you can't keep it
The latest version of RealPlayer has a download function that works pretty well on a lot of sites, allowing you to save streaming video as a Flash video file.
But those CBS developers are just a little too clever. When I tried to download a Trek episode, all I got was the commercial that played before the episode. Would've been funny if it hadn't left me so bitter.
Thus far, the only surefire ways I know to get a TOS episode is to record it from tv, or buy/rent the DVD. So 20th century!