Can a Mac Mini drive three monitors?
Alot depends on what Mac Mini you have. Early Mac Minis only had a single DVI out, later versions had mini DVI out, still newer versions had a mini DVI and a mini DisplayPort out, and the newest all metal version has a mini DisplayPort and HDMI out and comes with an HDMI to DVI adapter.

Negrino was correct in saying that you could get a USB to DVI adapter but you might only have to get one of them, depending on your Mac Mini's video out ports. If you have an early G4 or Core Solo Mini, you would have to get 2 adapters.

For a little clarification, are you planning on mirroring your desktop 3 times or having 1 desktop extended over 3 monitors? If it is the first option then you could simply get a VGA or DVI Y adapter that would mirror the image coming out of one port to 2 or more monitors.