Filezilla doesn’t just do vanilla FTP. It does SFTP and FTPS as well.
I personally use it to back up my wife’s blog onto my hard drive for easy disaster recovery or sudden webhosting changes.
There’s no doubt it’s one of the most direct methods to get/put data, but vanilla FTP is one of the biggest security holes remaining on the Internet as a whole. SFTP improves on that, but you have to have SSL compatibility on both client and server, which, believe it or not, is not always standard.