What do you use to diagram APIs to be built?

I'm leading a project where I need a remote team to build an API that's basically all in my head right now. I could write a bunch of documentation (and that's how I've done this in the past), but it might be better for them to see a diagram where I can show the resources and request methods to be used, then show a "behind the scenes" series of boxes and such explaining the database architecture along with the process.

There's gotta be some decent software for doing something like this, and I'm hoping some of it happens to be free. Any suggestions?

(Clarification: I'm interested in what YOU use and what you like, not just results from the first page of Addle - err, I mean, Google.)