How many monitors can be hooked up to a Mac Mini?
Only one Mac Mini (to date) has supported three simultaneous monitors. The Mid 2011 Mac Mini (Macmini5,2) came with an AMD Radeon HD 6630M that was powerful enough to drive two Thunderbolt displays while simultaneously driving an HDMI display. 1

The current Late 2012 Mac Mini, along with the other Mid 2011 Mac Minis, all have integrated Intel graphics that are only able to drive, at most, two Thunderbolt displays or one Thunderbold and one HDMI display.