Lots of games like that. I used to rent so many games, due to of course having no money but being allowed to rent 1 game every weekend. Could have bought every game I played and then some... for example I rented Halo 2 maybe 50-100 times. I finally got the game, and by then we were kind of bored.
I would say FFIV, but that was when I was like 5.
So maybe Vigilante 8 and its sequel. Rented it a bunch, great competitor to Twisted Metal.