Yes, you could. It is possible with wget or ncftp.
You just need to login to the server you want to transfer into.
Wget is more like a HTTP style download. For how to use it, check out http://www.lns.cornell.edu/public/CO.../wget_toc.html
NCFTP is a SHELL based FTP Client which allows you to copy or transfer files. It is more complex but it works. This is appropriate and can work on either the server you want to transfer from or transfer to.
For instruction on how to use ncftp , check out
Note : if you are using ncftp, all files would not retain the original ownership but that of the root or whichever user you log in as. So after you transfer, you will need to CHOWN them or else you might have trouble accessing them.
Alternatively, if you do not mind doing it without SSH but want to transfer server to server, you could always use WS-FTP Pro .