My favourite zombie films are Lucio Fulci's The Beyond [http://en.wikipedia.org/wiki/City_of_the_Living_Dead].
I like their Lovecraftian theme and zombies who are actually the dead brought back to life by occult reasons, like the gates of Hell opening.
David Cronenberg's Rabid [http://en.wikipedia.org/wiki/Rabid] is my favourite 'infected' type zombie film.
Dead Set [http://en.wikipedia.org/wiki/Dead_Set_(TV_series)] is my favourite light hearted, satirical zombie film. I know it was released as a series but I think it can be counted as a film.
Having to choose a popular zombie film from the list, I'd pick 28 Days Later. I think it's absolutely brilliant, but the reason it's not my favourite zombie film is that it's too close to home, a little bit too scary and I don't like to watch it very often (it's not as fun to watch as other, less believable zombie films set in America).