National is most known for this, if you're part of their program (free to join). Alamo shares the same fleet and is similar in design.
Budget, from recollection (although the PP may have more recent experience) does not, they assign you car.
Hertz uses a pre-assigned car, but offers Hertz Gold Canopy, and you just walk right to your assigned car. You have to be a Hertz Gold member (there is a cost, but there are many legitimate ways to get the fee waived). I mostly rent with Hertz, so most of my experience is with their service.
Thrifty and Dollar I do not believe offer this service on a regular basis.