Check to see if your transaction log files are being deleted by your backup software (only necessary if you have circular logging disabled). On the drive that is full, go to x:\exchsrvr\mdbdata and look for files named edbxxxxx.log (where xxxxx is a number in hexadecimal format). If you have lots of these files, circular logging is disabled, and your backup software is not clearing them out. When everything is working properly, immediately following an Exchange backup there should be one file named edb.log and four files named edbxxxxx.log. If circular logging is enabled, you will never have more than these files.
If you have this problem, set your folder view to display the archive bit. Delete all edbxxxxx.log files that do not have the archive bit set EXCEPT the four most recent. NEVER delete the edb.log file, the edb.chk file, or the four most recent edbxxxxx.log files! If this is not the cause of your problem, try running the optimizer as suggested above. This will only help if you have another partition (drive) that has more space than the one your database is currently stored on. If you don't have enough space on your server, you will have to add a drive to the system. Before doing that, ensure you have a full backup of the system.
You can perform an off-line backup by ensuring all folders starting with 'exchsrvr' are included in a standard backup. You cna find instructions for restoring an off-line backup on Microsoft's web site (support.microsoft.com).
Good luck.