Did you know that there are actually things to say about whether zero is even or odd (from Wikipedia)? Obviously it is, but the math-ed folks have seriously looked at this.
I found this via a comment by John Thacker at The Volokh Conspiracy. There's a poll there; right now 2% of people have said 0 is odd, 51% even, 43% both, 4% neither. I can kind of understand what's going on with people saying "neither" (perhaps they're getting this from some elementary-school notions), but how is 0 odd?
My answer: yes, zero is even, because it's twice an integer.
(Or because the identity permutation on n letters is an element of the alternating group An -- I've been thinking about permutations a lot lately. But if you understand that, you probably are like me, think zero is even, and didn't even think there was anything to discuss.)
Incidentally, sometime recently -- I forget the context -- I saw something that referred to the Gaussian integer a+bi as "uneven" if and only if a and b had different parity.