Well they run cars with 'em so it better be a pretty damn big lawn mower!
Biggest are in the range of 4kV 2kA, for industrial motor drives and other power conversion applications. Give or take whether you count just IGBTs, or include SCRs as well (they transist, but not in as straightforward a manner as IGBTs do). The biggest of any semiconductors are SCRs, pushing more like 7kV, 4kA, or probably more, I haven't checked in a while.
HVDC links are probably the most powerful monolithic application; with power ratings in the GW, they're constructed from stacks of semiconductors, I think usually SCRs or GCTs.
I'm not sure offhand if IGBT modules of that size are made from whole wafers, or many smaller dies in parallel. It does tend to be difficult to use large dies, over 2cm or so, due to differential thermal expansion between the chip and mounting base (typically Cu and AlN). The "puck" modules get around this by sandwiching the die between molybdenum pads, which has similar expansion rate, but the sandwich versus a metallurgical bond (I think, unless they are soldered or otherwise bonded as well; I forget) relieves thermal stress, permitting quite large dies to be used (~whole wafer).
Tim