Sure can, man.
You just have to check your clearance from the suspension and fenders and stuff like that.
If your stock rear wheels are really close (like 1/8") from the inside of the fender at any point throughout it's upward and downward range of motion, I'd steer clear of getting bigger tires. Usually, though, you can go an inch or two bigger in diameter before getting too close.
Of course, you could always trim your fenders, but if you're like me, that's not really an option.
As for the fronts, just make sure that nothing's going to hit anything height or width-wise.
That said, you should be good to go.
Check out
ATVSource,
ATV Connection,
ATV Time, and
ATVFrontier. Chances are, someone's got an Eiger they've put bigger meats on, not to mention maybe a lift and some other goodies!