Dropbox is a very handy system for sharing files online or sending files to friends that are too big to attach to an e-mail. The free Dropbox program uploads them in the background to the dropbox site, while you're doing other things on your computer. Once the upload is complete, your friends or anyone else that knows the exact link, can download them.
You get 2 GB of free space. That's more than enough for me, so I've never needed to become a paying user. When you signup and mention who referred you, that person gets additional free space - if I remember well.
People have found many creative uses for Dropbox. They use it to automatically backup files to, to sync files (bookmarks, documents, etc.) between pc's, to access their documents while on the road, etc.
My only complaint is that it tends to make my pc unstable after a while. But that's no problem, I only run it when I need to upload something and I reboot the pc when it's done. I wouldn't recommend running it permanently though.
[EDIT: I rarely reboot my pc; people who shutdown daily may not see any problems]
As a cheapskate who sometimes needs to share large zipped photo archives, I love Dropbox.