Backing up a really huge SQL Server database
If you do not have enough diskspace first confirm that you have backup compression enabled. This will greatly decrease the size of your database backup. If you still do not have enough space on your server to put your backup.

I see 3 options of achieving this


Try backing up to a network share which has sufficient diskspace to store your database backup


--> If you do not have enough space on a networkshare 


Try backing up to different files on different drives/networkshares so you split the total size of the backup and store all the parts on different locations. This will also increase the speed of your backup
(Check out http://www.mssqltips.com/sqlservertip/935/backup-to-multiple-files-for-faster-and-smaller-sql-server-files/)


--> If you still do not have enough space on any server/share/...


If you can physically reach your server, go buy a USB disk with sufficient space and connect this to the server and backup to this location.