You might want to check out FUSE for Linux. There are various programs built on top of it which allow remote filesystems to look exactly like local ones. Two that I use are curlftpfs and sshfs. It's really nice to be able to perform any of my computer's programs on these remote files, and it looks very similar to what Dropbox accomplishes. Of course, you would need to have an FTP or SSH login somewhere, but you can get free FTP access from e.g. Lycos, so that shouldn't be an issue.
In short, I guess I'm curious what separates Dropbox from using a free FTP service which is connected either through Windows' built-in Network Places or Linux's curlftpfs. There are obvious differences, but are they enough to warrant fees?