Mixing tires is pretty common for off road bikes without suspension. Running a big tire up front gives a little bit more comfort/traction/pinch resistance for bumpy trails. I ran a 2.3" front and 1.8" back for a while.

On the street, it could help prevent pinch flats from curbs and potholes. But I get most of my pinch flats on the back, so thats where I'd put it.

I've got the impression that for general riding on the street, using different tire sizes won't really make a noticeable difference, or at least not a noticeable improvement. But experiment away and let us know if you come across anything.