Arguably, zero is neither. Zero disobeys many rules that we usually ascribe to numbers. It is also feasable zero is not a number at all, but the absence of numbers, in the same way that black is the absence of color.
As it is between two odd numbers (1 and -1), it could be classified as even. It is not, however, divisible by two as all other even numbers are, so therefore it may be classified as odd. Since neither can be agreed upon, zero is neither even or odd. It's just zero.