As Ben said, there are two definitions.

[link|http://whatis.techtarget.com/definition/0,,sid9_gci284008,00.html|Here]:

A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways:

N = {0, 1, 2, 3, ...}

N = (1, 2, 3, 4, ...}

The Number Pope (or is it Cardinal Number?) hasn't ruled which is correct. :-P

Cheers,
Scott.