Say you're counting the length of a fence, so you are numbering the posts. Of course it's preferable to number the posts starting at zero, because after having numbered N posts, you know the length of the fence is N.
On the other hand, if you are counting the posts themselves, you would want to say "one!" after the first post, as you have just counted one post. In this case, the number you assign the post is the number of posts counted after encountering it. Otherwise you end up having to +1 at the end.
Which is all to say: I've always felt that the disagreement between whether to start at one or zero is due to people not making clear what it is they're counting.
If you're numbering the points between spans (as you tend to be when giving names to dates, memory locations, and fence posts), always start at zero. If you're giving numbers to the spans themselves, it's often convenient to use a physically-based number such as the location of the center of the span (when writing graphics applications I will often refer to the pixel in the upper-left corner as 0.5,0.5, rounding down to get its address).