I have seen bikes with a disk brake on the front and rim brakes on the back. Most of your braking is done with the front so it makes sense to have the best brake up where it'll do the most good. I wouldn't want a disc on the back as the back is more prone to skidding so less capable braking on the rear makes sense.

A motorcycle is the same situation. When you brake, inertia is going to put much more of the weight towards the front of the bike. Having a lot of braking capability on the front is going to provide much more stopping power than on the rear where the weight is much less during braking.