Fallout is a legendary computer role playing game. Set in a post nuclear world, it has a 1950s science fiction aura. Here’s a miniatures game set in that world.
Scavenge Skirmish Survive is a set of free wargames rules for a tabletop game set in a post-apocalyptic volcanic winter. Link goes directly to a pdf
Michael Taylor has written Road Warriors, a set of free wargames rules that uses Matchbox cars for games set in a post-apocalyptic future, ala Mad Max.
Urban Warzone is a set of free wargames rules for near-future urban combat in a post-apocalypse world.
The author writes:
Wasteland is a game of post-apocalyptic warfare between small bands of desperate fighters. You can play it as a skirmish war game using the character archetypes and weapon lists but it’s also designed to allow you to play fast-moving and memorable campaigns with two or more players.