Executing Arbitrary Code at a Specific URL without Creating a Post or Page?

@Hi Beau Simensen:

The hook plugsin_loaded is one option, but you can use the plugin I posted for this question to see what plugins are run and in which order and use it to find the hook that works best for you:

Given your goal, you might also find this answer useful:

If that wasn’t what you needed please elaborate and I can hopefully offer more.