Motorcycles differ from cars in at least one crucial aspect -- cars ride on the flat portions of their tyres, and motorcycles do not. Though some of the big tyre versus small tyre arguments still apply, there are a few very important differences.
A wide rear tyre means more tread on the road, making the motorcycle want to push through turns instead of go around them. This can lead to a dangerous under-steer condition.
Wider front tyres will have the opposite effect of a wide rear, and can make the bike more responsive in the corners (over-steer). Caution is advised, however, because a wide front tyre combined with a motorcycle's short wheelbase can make for a twitchy and dangerous ride.
Some bikers prefer a narrower tyre on both the front and back, because the tread of the tyre is more pointed and handling is a little more crisp. This can, however, lead to serious instability problems at high speed.
The best solution is to go wide on both ends, since overall grip will be increased and the handling balance retained.
In general, a rim can only use tyres 10 mm (0.4 inch) wider or narrower than the stock tyre. Exceeding this window can result in pinch flats, increased tyre wear or blow-outs.