Steven,
*Interrupting A Time Machine Backup*
Just make sure your computer shuts down first, and
then cut the power to the Time Machine drive. If the Time Machine disk shuts off during a backup it could cause problems later.
This KB article discusses backup interruptions related to the Time Capsule, but the information can apply to other Time Machine hard disks as well:
[http://support.apple.com/kb/HT1176]
Generally, Time Machine is smart enough to pickup where it left off when a backup is interrupted. It deals with the procedure of a normal shutdown or sleep with elegance. But if the backup process is interrupted by a system crash or some form of power interruption, then anomalies are introduced requiring TM to perform a "deep traversal". Since the average incremental backup only requires about 2 minutes, it shouldn't be that much of an inconvenience to just wait for the process to finish.
As for "stopping" a backup, either using the TM menu or clicking the little "x" icon in the TM preference pane will work and should not be considered a dangerous interruption.
*If Time Machine Backup Disk Runs Out of Space*
Are you sure Time Machine hasn’t lost track of your backups and isn’t trying to perform another full backup of your system? This is likely if Time Machine has stopped “pre-thinning” your backup drive before attempting a new backup. You can determine if this is the case by watching the backup attempt in Console.
If it is attempting to perform a new full backup, it may be possible to re-link Time Machine to the old backups again if this is the same computer that generated them to begin with.
On the other hand, your computers drive contents may very well have outgrown the capacity of the Time Machine backup disk. It may be time to purchase a larger capacity hard drive for Time Machine backups. Consider as well: Do you really need ALL that data on your primary hard disk? It sounds like you might need to Archive to a different HD anything that's is not of immediate importance.
You see, Time Machine is not designed for archiving purposes, just as a backup of your local drive(s). In the event of disaster, it can get your system back to its' current state without having to reinstall everything. But if you need LONG TERM storage, then you need another drive that is removed from your normal everyday working environment.
Does that make sense?
This KB article discusses this scenario with some suggestions including Archiving the old backups and starting fresh:
http://docs.info.apple.com/article.html?path=Mac/10.5/en/15137.html
Hope this info is helpful.
Cheers!