As a developer aid, both for C developers and Python ones, it is very useful for debugging to be able to see the indices of vertices, edges, and faces.

Crouch has an external addon (see https://sites.google.com/site/bartiuscrouch/scripts/index_visualizer_25) that does this, but there are issues that have prevented it being included in contrib. This is a C patch that does a simplified version of the same thing.

What it does:
In edit mode, if you open the right hand 3d space property panel, I added to the Numerics section an "Indices" checkbox. If you check it, then any selected vertices, edges, and faces will have their numeric index (their position in their respective lists) drawn near them on the screen.

I recognize that this is a capability only useful to developers, and probably confusing to non-developers, so it is only enabled (and the checkbox only appears) when blender is started with --debug.