It is hard to defend 0-base without programming a lot of array-based code, such as string searching and various sorting/merging algorithms, or simulating multi-dimensional arrays in a single-dimension array. Fortran is 1-based, and you need a lot of coffee to get this kind of code done right.

But it goes way beyond that. It is a very useful mental habit to be able to think about the length of something rather than the indices of its elements. For example, in doing pixel-based graphics, it is much clearer to think of coordinates as falling between pixels rather than on them. That way, a 3x3 rectangle contains 9 pixels, not 16.

A little more far-fetched example is the idea of look-ahead in parsing, or in printing sub-totals in a table. The "common-sense" approach says 1) get the next character, token, or table row, and 2) decide what to do with it. The look-ahead approach says 1) assume you can see it, and decide if you want it, and 2) if you do want it, "accept" it (which allows you to see the next one). Then if you write out the pseudo-code, it is much simpler.

Still another example is how to use "goto" in languages where you have no choice, such as MS-DOS batch files. The "common-sense" approach is to attach labels to blocks of code to be done, and label them as such. Often a better approach is to put labels at the ends of blocks of code, for the purpose of skipping over them. This makes it "structured" and much easier to modify.