Since zero is the lowest value of an unsigned binary integer, which is one of the most fundamental types in programming and hardware design, it is often natural to count from zero rather than one, especially when the integer is actually an index, as in hardware addressing or c and lisp's 0-based indexing of arrays.
Hackers and computer scientists often like to call the first chapter of a publication "Chapter 0", especially if it is of an introductory nature (one of the classic instances was in the First Edition of k&r). In recent years this trait has also been observed among many pure mathematicians (who have an independent tradition of numbering from 0).
Zero-based numbering tends to reduce fencepost errors, though it cannot eliminate them entirely.
Logically, the next item after the zeroth should be the "oneth" but this is never used.