As Shokhead said it is the type of tires not the bike. I have a road bike with 23mm Michelin Axial Pros. 3000km on this bike last summer, not one flat.
I have a touring bike (actually more a 'bad wheather bike') that has a lower quality Continental 1000 series tires. 2000km - 2 flats. But still quite a good track record.
If you could not find any glass, nails, etc in your tires (sometimes you don't) and you are getting alot of flats and don't see any reason why, it could be any number of other things than the tires. No rim strip or frayed rim strip perhaps? Pinched tube between the tire and rim? Something inside the tire chafing the tube?
Digger