I lived in a smaller town when i was younger and we rented video games from the grocery store. I recall n64 games on one side of a display rack, and vegetables on the other.
Our household used to rent RUSH 2049, Vigilante 8, and Gauntlet often. Many fun weekends to be had!
Sonic 2 and on were common rentals of mine. I also rented Dune Battle for Arrakis a lot. I finally purchased a copy in the early 00s. But I think the game I rented the most was Another World, and there was another one of similar concept around the same time (which I think was a genesis exclusive) that I rented a lot.