The guys at tivocommunity have a nice FAQ up about how to upgrade your TiVo Series 3 with an external eSATA drive. Although it's not "officially supported", with the maximum 1TB external drive in addition to the internal one, you can get a good 1.25TB chunk of space to hold all your shows.
Head over to the forums to find out which drives and enclosures have been confirmed to work—which should be updated frequently—and various other gotchas you should look out for when doing your own upgrade. Brian will get right on it as soon as he's done cleaning the bodily fluids off.
Series 3 Upgrade FAQ [TiVo Community]