It kind of goes from one extreme to the other. All will ask you to list schools you are considering.
The NROTC award is to a particular unit. If there are cross-town schools associated with that unit, they are all considered as a single unit. They ask you to list several units - not colleges. In our case, it meant that U of Michigan was the unit, and since Eastern Michigan is part of the crosstown, it couldn't be used as another college. Transfers from unit to unit can happen, but are not guaranteed. I'm sure some NROTC people here can clarify that.
AFROTC national scholarships can be used at any detachment. Therefore, a detachment can end up with three contracted freshman one year and thirty the next. They do ask for schools - but the award does not need to be used at a school you have listed on your application.
AROTC (I believe) awards to particular schools from your list. Say you put down 5 colleges - they may say you can use the award to one of these 3 schools. It is possible, again, to transfer the scholarship if both units involved are in agreement. From what Clarksonarmy has written, that does not seem to be prohibitively difficult.