If you're okay with waiting a few hours/days, The Pirate Bay seems to have a good selection of torrents of recent Jeopardy! episodes, though I've not yet tried it.

You'll also be able to see a full transcript of the board, as well as all questions provided by contestants, at www.j-archive.com.

Found http://www.youtube.com/watch?v=BfNBWJTGEEA and it is good quality.

Looks like IBM will have it online in a few days http://twitter.com/#!/IBMWatson/status/37223337453158400

I had thought from the counter that IBM had run on the Watson page that there might be but it seems that us non-US residents will have to wait. Still very much looking forward to this. History in the making.

Hulu refers to crackle.com. Crackle has "minisodes" which seem to date from 2002-2003.

It is owned by Sony, distributed by CBS and seems to be syndicated, which means there is no network that carries it specifically, and thus no online distribution, as each market has a different station (Eg: Fox might buy it in one market while ABC might buy it in another).

This is near as I can tell looking into it.