Saying the 28 Days/Weeks Later movies aren't zombie movies is bullshit. Yes, the infected may not technically be zombies, but beyond that, they have far too many elements of the typical zombie apocalypse movie to be considered otherwise. You could say that they're not technically zombie movies, but that they are fucking zombie movies.
Dawn of the Dead is more or less the quintessential zombie film. Day of the Dead and Night of the Living Dead are also very good. Zack Snyder's Dawn of the Dead remake is also recommended. Land of the Dead is okay, stay away from Diary and Survival.
Pontypool and Deadgirl are two flawed but interesting and original takes on the zombie genre. It is perhaps best not to think of them as zombie movies at all.
Some good comedic zombie movies are Braindead, Shaun of the Dead, Re-Animator, Wild Zero, Return of the Living Dead,