After the original Night of the Living Dead, Shaun of the Dead is the best of the zombie movies. It works very well as a comedy and as a horror movie. Simon Pegg and Nick Frost are excellent as a pair of slackers in London who don't realize when the zombie apocalypse starts.
When they finally figure out what's going on, the movie shifts from comedy with a few zombies to zombie movie with a big dose of comedy. Be warned, however, the last act of the film is darker than you might expect, with both sad moments and some zombie horror elements.
For the few people who haven't seen this masterpiece by Edgar Wright, Shaun of the Dead is highly recommended.