To me, zombies are the ultimate horror monster because they are such a metaphor for the inevitability of death. It is slow in coming (relatively speaking); it can't be stopped, only slowed down; and it is indiscriminate- it doesn't care who or what you are, it doesn't even consciously seek to destroy you for any reason other than that's what its purpose is.
For those reasons, I like my zombies "classic" style- slow moving, ignorant of any damage suffered short of complete destruction, and mindless. None of that fast-moving stuff for me.
Serious is cool, but a lot of the best zombie movies don't take themselves too seriously either. Night of the Living Dead is a classic "serious' zombie flick, as is Day of the Dead. Like Romero's less serious Day of the Dead, though, both also manage to convey social commentary, which is cool. Shaun of the Dead, for all its tongue-in-cheekness, still manages (early on in particular) to have some of the most creepy zombie scenes (the scene in the grocery store was pretty cool- he's slipping on something, and you don't even have to see what it is to know what it is, not after seeing everything else going on around him. Sweet.)