Dropbox + Solr = full text indexing and search for files in your Dropbox. I wrote an app in Sinatra that authenticates to Dropbox, downloads your files, and indexes them in Solr. It also provides a simple interface for searching that includes hit highlighting and some basic facet support.
I've posted the project on github, so feel free to download and try it. For anyone interested in this as a hosted service instead of as a download and install, let me know.