What I love about Dropbox is that you don't have to check in/check out every time you make the slightest change. The versioning is implicit, which is the way it should be for most personal files (although it would be a disaster for SCM).
I've been using Dropbox to sync shell configuration files across several (4+) machines and it's a dream come true. I now have versioned bashrc files, my vim plugins, on every machine.
SVN is for version control of files. Dropbox is simply for sharing/syncing files where you don't need a full history.
I use it on my laptop/home/work computers. If I have a file I need on another computer rather than vpn into work and send it over or ftp into a server and drop it there to pick it up later I just throw it in the dropbox and it syncs to all computers. It's nice.
EDIT: Forgot to mention that dropbox does keep a version history of your files. I just don't use that particular feature.
You could get basically the same service, but uglier and slower, via webdav_svn and Trac. I did that for a while back in ~2005, but man was it slow. Maybe today, you could use Git with a cronjob that autocommits, pulls and pushes every minute or on mtime changes.
