Yahoo! just announced My Web 2.0 and I'm happy to confirm that there's a webservice to go with it. My Web 2.0 is, among other things, a tagging platform, and the three webservice methods enable you to slice and dice the public tags in a whole variety of ways.
tagSearch - Find out what tags have been applied to a URL, or what tags people are applying in general.
urlSearch - Find URLs that have been tagged in a specific fashion.
relatedTags - Want to know what other tags users have been applying to sites tagged with 'yahoo'? Or 'music'? Both? This method will let you do that.
All the functions will let you filter by a Yahoo! ID, so you can look at other people's public tag space and see what tags they like to apply, and when. Or use it to show off your tag space wherever you want.
There's a ton that can be done with just these three functions, but if there's something else you'd like to see in the webservices, let us know in the comments. In the meantime, check out My Web 2.0 and start tagging and sharing!