People who own houses and apartments usually do but rented places often have shared laundries. In newer buildings every apartment has its own laundry.
It's pretty common to have a shared machine in the basement. If you're lucky, it's on the -2 sublevel somewhere in a nuke shelter (yes, literally) and nobody cares whether you use it at 3 am on a Sunday.
I think it also depends where you live in Switzerland. From foreigners complaining about it I deduct that Zurich tends to be relatively strict. Where I live (Espace Mittelland) this is a non-problem.
People in small apartments usually don't, people in houses always do - this is the same in the US though.