mixing/matching tires

Most bikes come with identical tires front and rear. This is all right for general use, but if you want to optimize your bike, you should consider using different tires front and rear. The front and rear tires have different loadings and different requirements.

Narrower Front, Wider Rear

If lightness is the primary goal, tire width/weight is limited by the risk of pinch cut flats, a.k.a. "snake bites." Since there is more weight carried on the rear tire, you can get away with a slightly narrower tire in front than you can in back.

Wider Front, Narrower Rear

A wider front tire makes sense in many applications, however, when handling and ride comfort are considered. A wider tire will generally provide better cornering traction than a narrower one, assuming appropriate inflation pressure. 

A wider tire also provides superior shock absorbency. I personally prefer a slightly wider tire in front, since I suffer from some wrist discomfort on occasion.

Off-Road Issues

Bikes that are used some of the time on loose surfaces often benefit from a wider front tire, with a fairly agressive tread, coupled with a somewhat narrower, smoother rear tire. 

The wide, knobby front tire will provide the all-important front wheel traction. If your front tire skids, it almost always leads to a crash. For riding in soft conditions, such as sand or mud, a wide front tire is essential. If the front tire sinks in and gets bogged down, you're stuck. If the front tire rolls through a soft patch OK, you can generally power the rear through to follow it.

The narrower, smoother rear tire will have lower rolling resistance. Since most of the weight is carried by the rear tire, rolling resistance is more important on the rear than the front. If the rear tire slips, in most cases the worst that will happen is that you'll have to get off and walk.

This is a great idea that developed out of BMX racing.

Some mountain bike tires come in matched sets, with diffrerent tread front/rear. The front tires tend to have the knobs set up more or less parallel to the direction of travel, for improved lateral grip and better steering control. The rears tend to have transverse knobs for driving/braking traction.

source: http://www.sheldonbrown.com/tires.html