The Programmable Web reports that as of Nov 2008 it has 1,000 Web APIs on its directory.

You can see the distribution below (which looks pretty balanced all around) with Mapping APIs at the top:

And what is the preferred way to expose and consume Web APIs? The following chart shows REST at the top, with SOAP second:

(my recommendation, to use RESTful calls and XML Feeds, and consider JSON for mobile-to-server Data Interchange)