Backup database directly to FTP server
If you just want to backup to a non-network path location, then there is now a [tool for backing up to Windows Azure.  Also, SQL Server 2014 will allow to backup directly to Windows Azure without a separate tool. This is a viable alternative to trying to backup to a FTP site while eliminating the need to keep a local copy of the backup. Please note the backups can be encrypted which is an obvious must if you are storing the backups off premises.

Otherwise, you may want to find a way to map a FTP site as either a network path or drive.  Although I have never used either of these products, FTPUse and NetDrive should allow you to accomplish this goal.  There's a blog post on how to map FTP sites as network drives in Windows 7 that might also work for you, but it appears to be an OS-specific solution that might not work for you.

Although these solutions may work, I would strongly recommend that you backup the file locally and then copy it to a FTP site.  Drive space is cheap.  If you store the backup locally, then you can easily restore from backup without having to download the backups.  You should also periodically test restoring your backups to validate that you have good backups.  You should also periodically test restoring your backups from wherever you are sending the backups to make sure these are good as well.

Backing up a database is an IO intensive process and backing up to a FTP location even if it is represented as a local drive will probably be very slow.  Even if the performance is adequate for your purposes, FTP connections can be unstable and can be interrupted for a variety of reasons.  You don't want to have to run another backup just to get the file over the to FTP site.  It would be safer to backup to a high speed local drive and upload the file separately.  I would strongly recommend finding a way to solve your storage problem rather than going down this road.