Global Game Jam takes place yearly, the last weekend in January. There are sites that participate from around the world, so it really is global. I've participated/helped run the event for the last four years. Sites should be starting to register themselves soon, so check the site to see if there's a local event in your area.
Ludum Dare happens 3 times a year, and is all online. There are two events the compo (competition) and the jam. You can read up on the differences, and find dates on their site. I've only participated once, largely because I don't always have the time when it's taking place.
@Kae Given that your Hack-a-thon students were interested in games, maybe you should encourage them to go to Global Game Jam. :) Better yet, if you've got the interest, see if you can host your own site. I know someone was trying to get a site going at CU Boulder last year, but couldn't navigate the bureaucracy in time. There is interest up there.