Super alternatively, there’s FireFTP, an FTP client/addon for Firefox. I never use it because I’ve never had a reason to have an FTP client in my browser.
If you’re just looking to back up files, you can use Mozy or Dropbox, or Gmail Drive, which, well, creates a drive out of your Gmail inbox. I wouldn’t use that if your files are really important, though, because Google could cut the cord anytime they wanted to.
FireFTP has the same issue. Starts off uploading fine, then my upload speed drops to below 1 kb/s. I guess they block pretty much any outgoing FTP traffic. Though I wonder if it’s different for people on the residence network. But I can’t get on that.
As far as Mozy and dropbox and stuff, what I’m making is less a backup for myself and more of a repository for others to see. I.e. I upload the awesome notes I have yet to take about my new psychology chapter (learning) and everyone learns some awesome stuff. Also for giving my notes out to people who couldn’t come to class. So it has to be publicly accessible.