The general trend is that we store more and more information no longer on our own computer, not on a server we control, but we give our information to a completely foreign company that does even reside in a different country. We give away the control over our data and often we can't even process that data anymore like we were used to.
But there are APIs, and these APIs do allow really cool things and some webapps do already allow cool things (e.g. you can import a table from Wikipedia in Google Spreadsheets and reexport it with Yahoo! Pipes and display the geographical information that was in that table using Google Maps, here is a German explanation how to do this). But let's bring it back to the basics - why can't we use the programs we are used to with our data that's elsewhere? Well, because it's not in our filesystem. But what if we could change that? And yes, we can.
There is flickrfs that allows you to browse photos from Flickr in your (Linux or Mac OS X) filesystem, and with gdatafs you can do the same with Picasa from Google. And for Google Docs, there is something similar: GDocsFS, though I am not sure if it already supports writing documents. In the Windows world it's a bit harder, but it seems there are efforts, to make things like flickrfs work on Windows, too.
There are also smaller things (compared to Flickr/Picasa) you can bring into your filesystem - like Wikis, including file uploads, for MediaWiki there is fuse-mediawiki, for DokuWiki my own, still under development DokuFS or Delicious, though I am still missing the real idea what to do with bookmarks in the filesystem (if you have any, please comment!), a prototype does already exist (but still read-only), see here.
In most cases we won't get our data back, in some cases we really can by copying the directories to our harddisk, but in all cases we get a lot more possibilities and apart from that, it's a lot of fun.
There are probably many more examples and yet more ideas what to with fuse and web-apps that have APIs, I would love to hear your thoughts!