There are a lot of superhero miniatures rules out there — both free and commercial. So if you want to try one without going to all the trouble to paint some minis, you could try some of the paper figures on this page.
Tabletop Titans is a set of free wargames rules for superhero miniatures games.
Pulp City is a set of free wargames rules for pulp, super hero, tv series and B-Movie adventures.
Marvel Civil War Skirmish is a miniatures-and-cards game based on the airport battle in Captain America: Civil War. It is played on a checkers or other 8×8 board.
Clobberin’ Time is a set of rules for fast superhero skirmishes.