0-based indexing has the advantage of easily mapping to memory addresses since the index is an offset from a base address (perhaps multiplied by a unitary per-item length). I personally prefer this since I tend to think about and work with data as an offset from a starting point.

1-based indexing has the advantage of always knowing the length of the array since the index of the last element is this value. You also get "proper" counting numbers as you iterate.

I've used both in various languages. Perl lets you define the array index start to be whatever number you wish.