In my experience it's about 50/50.

On adv purchase bookings half take the money immedietely and the other half don't bother until check out.

I have noticed that Crowne Plaza's will always take the money as soon as possible, at least in the UK anyway.

Intercontinental hotels vary too, recently Hanoi took my money 2 months in advance but Bangkok and Hua Hin did not ask for payment until check out.