Avis has avisfirst (www.avisfirst.com) where you can get a free weekend rental coupons for every X rentals (I don't remember the number but the details are on the site). The biggest drawbacks of the system are:
1. You don't get credit toward free weekend coupons if you collect hotel/airline points/miles.
2. There are usually long blackout periods where one can't use the free coupons.
3. You need to have a Saturday night stay to be able to use the coupons.

Most people just elect for airline miles, that I know of, but everyone's case is unique.