When I hear "File Transfer", I think FTP (File Transfer Protocol).
FTP is probably the most mature technology, with the most options on all platforms.
After you configure an FTP server, Konqueror allows you to simply "Add a network folder" to it. Then, it's all drag and drop. Windows will allow you to do the same thing in pretty much the same manner.
In addition to that, pretty much every web-browser has ftp support built into it natively. So, you can upload/download them without even adding a network folder. Also, there are some great FTP plugins for Firefox, like FireFTP that allow for even more features.
And, of course, it lends itself well to shell scripting too.