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Don't use your primary internal hard drive, i.e. don't partition it and put a backup on the partition. Disaster recipe for certain.

Your solution is either an online backup, like Mozy.com or Carbonite.com, get a time capsule, or get a hard drive. Hint: get a drive with firewire 800, it makes a difference. If you're lucky enough to have a Thunderbolt port, get a Thunderbolt drive, it is the ultimate.
 
Burn optical media with the critical documents or data that you need to backup.
Backup to a flash drive and copy to another computer/HDD.
As mentioned above an external HDD is the best way to go.
Having 2 is better: one for time Machine and other for a clone.
 
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