Well, board game or table top game?
40k is a bit different than Zombicide, but either way:
For table top, I'd take a look at X-Wing. It's simple enough that my buddy plays with his 6 year old nephew. Models are pre-painted, so no worries about that.
For board games, I'd take a look at most anything Flying Frog puts out:
Last Night on Earth: the Zombie Game is basically a zombie horror move in board game form. The rules are pretty straight forward to start, but can get pretty complex if you opt to use some of the expansions. The game itself is pretty tongue-in-cheek and light-hearted. It's one of my favorite games right now. Fits 2-5 players, zombie player(s) vs survivor player(s).
Fortune and Glory is another Flying Frog game I really love. Think Indiana Jones the board game. You can play coop or competitively; you race around the world trying to collect artifacts before the bad guys (Nazis, Mafia or Order of the Crimson Hand) do. It's a big game, with lots of components and a bit of set up time, but it's really fun. Fits 2+ players, but starts getting unwieldy after more than 6 I'd say.
Betrayal at the House on the Hill is by WotC/Avalon Games. It's a pretty fun take on the "haunted house exploration" theme. You start off as a team exploring a house and building the board as you go. Eventually the Haunt triggers and one of the players turns against the others (determined by the events of the board building). Then it's a race for the heroes to defeat the traitor before the traitor can finish their schemes. It's a pretty popular game among my friends and I. Plays 2-6.