There are several games out there. I know of the following:
Zombicide - Technically a board game, but each character has skills. They gain experience during the game to learn new advances. There is different equipment, searchable items to get more equipment. It can be co-op or competitive. This one is fun with all the various missions in the sets. It can get very difficult depending on the zombie spawns. It is by Cool Mini or Not.
Walking Dead All Out War - It is competitive for two players. It is based off the comics. The rules are simple, but there is some strategy to the game. It is alot of fun. This is by Mantic Games.
Project Z - I do not know much about this one. It is by Warlord Games.
Zombies!!! - This is a very simple random board type of game. The rules are super simple, but it can be fun. The expansions allow for different types of zombies.
Last Night on Earth - This is a board game similar to Zombicide. It seems to get good reviews, but I have not played it.
Savage Showdown - It is skirmish rules using the Savage Worlds rpg. It would allow you to create any type of skirmish game you might want. I have not played it, but I have played the RPG. It would seem to make a perfect skirmish game.