Is there a program that can FTP from one server to another?

Basically, I have a large number of big files that would take forever to download from one of my servers and then upload to another. Is there way to directly transfer the files from one to another?

 

FlashFXP can do that.

But your servers need to allow FXP, meaning transferring files from one to another. Most hosts dont allow that.

 

I run both servers. How do I enable that?

 

There is a program called Mysql Tools 5.0 or new.. Try it.

 

just try first and see what happens: flashfxp.com
if it doesn't work then search the net and see how to enable it
i guess it depends on what type of server you use

 

Use flashfxp. You meed to make sure your server's ftp program supports site to site transfers (FXP)

 

If you run both servers and have shell access, just use ftp from the shell or setup rsync.
Even without shell access you might be able to setup a cronjob script to ftp the files.

You really need to provide more server information to get better responses.