Well for one, most situations I can think of when an index is calculated a 0-based index is more useful.

Addressing an element T[h][w][c] in a linearized 3D tensor with 0-based indexing:

    T[h*W*C+w*C+c]

with 1-based indexing:

    T[(h-1)*W*C+(w-1)*C+c]

Or let's say you want to take a string "abc" and repeat it until the length is 10, getting "abcabcabca". With 0-based indexing:

    a,b = "abc", [" "]*10
    for i in range(0,10):
      b[i]=a[i%3]

In a 1-based language that's:

    for i in range(1,11):
        b[i]=a[(i-1)%3+1]

Here's what Dijkstra has to say about it:

http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EW...