I use my debit card everytime I rent with Alamo... I don't know about any others, but I'm sure there are some more out there. Here's info from Alamo's site-
"When renting in the U.S., debit and check cards may only be used in conjunction with proof of a round trip travel ticket (airline, cruise ship or train) at time of rental.
A debit/check card is considered to be any non-credit card bearing the Visa or MasterCard logo. Any other non-credit card without the Visa or MasterCard logo is not accepted.
For pick-ups in the United States, without proof of roundtrip ticket, debit or check cards are only accepted when returning the vehicle. A credit card in the name of the renter must be presented at the time of pick-up (unless city specific exceptions apply as stated below.)
All Alamo locations in Manhattan do NOT accept debit cards at the time of rental. They are accepted at the time of return only
Alamo locations in Canada will now accept debit cards for payment at the time of rental if the debit card was issued in the U.S., and if the renter has proof of round trip travel.
Debit cards that are issued in Canada are not accepted by Alamo at the time of rental or return."