That's a matter of some debate. Mostly, the standing of zero is considered to be a matter of consensus. There are some properties a number must have to be considered natural (or integer, that's not much different). Zero either does or does not fulfill these, depending on how you treat it (this ambiguity would normally not be possible, but zero does have certain unique and problem-causing properties, e.g. the problem of division by zero). Therefore, you may encounter differing views in different /scientific/ publications.
However, the consensus regarding natural numbers is almost always that zero is not natural. This is mostly because many definitions and theorems use operators that should cover the range of positive integers from 1 to n (a general integer), like, say, a finite sum from a1 to a(n). It is more practical when you can write "for n of N" (N is natural numbers), but since that would not work if zero was included in N, it usually is not.
However, the aforementioned ambiguity applies in full to the question of whether or not zero is an integer. lillian was here