Public web applications, especially those that allow exporting my data in easily processed formats, have been the most important changes in the way I use computers since I made the transition from punched cards to a Dec-10 in the 1970s, when I bought my second home computer in 1978 (serial #71 Apple II), when my company SAIC bought a Xerox Lisp Machine for me in 1982, and I started using the Internet in 1985. I now use GMail, Google Calendar, Blogger.com, Flickr, Google Documents, Gliffy.com, Google Reader, Picasa web photos, and del.icio.us as a regular part of my work process and for entertainment.
The key thing is that all of these public web services allow you to export your data for archival backup, use in utility scripts and programs, etc. Most also support, in addition to manual data export, web service interfaces.
The only work that I perform “locally” is programming in Emacs+Common Lisp, various languages in Eclipse, and writing large documents using either Latex or OpenOffice.org. Even for “local work”, all of my working materials are stored on leased managed servers in subversion repositories.