The most recent clips are on the comedy central website, though those don't stay up very long.
There are at least four different groups that I know of that put up torrents of both shows every time the air. Last time I checked you can only get the iTunes selections for a couple of weeks back; you can find TDS and Colbert from several months back via torrent. Every so often, people will even post compilations of all the segments from a month.
There are a variety of locations for that, but a good place to start is the Canadian site iso hunt or the dastardly Swedes at the Pirate Bay, both of which have recently weathered encounters with the MPAA. Latebyte, a Norwegian site that specializes in US Late Night TV shows (Leno, Conan, and, of course TDS and Colbert) is the most logical place to look, but you have to navigate the registration process in Norwegian. And if you're really serious, you can try to get an invite to Demonoid or one of the restricted registration sites. But most of their torrents are available on ISO anyway.
-s