The operation of my computer (Mac OS X 10.6.8) has been frequently interrupted by an unexpected shutdown. How to solve the problem?

Dear Sirs, owners and managers
Apple Support:
I appreciate the opportunity given to request either always valuable assistance of masters.
It happens that I have been supporting, for some time, inopportune and unexpected shutdowns
of my Mac, with losses mounting and haul what I write in TextEdit.
I ask, in this situation indigestible, a help of you to resolve this anomaly and thus be able to
take back a firm and smooth operation of the MAC.
Sincerely,
Ricardo Cutolo

Given your problem statement:
inopportune and unexpected shutdowns of my Mac
Unexpected hard shutdowns are usually either severe operating system corruptions, or they're triggered by hardware errors.   Bad memory, bad processors, bad power, bad disk, bad main board, etc.
A likely first step is to archive (back up) your data onto an external disk.  Get a good backup. 
After that (and possibly a second, verified, external-disk backup), check your system log for any potential clues that might be logged there.   If there is nothing obvious, then ensure that all external devices (other than a keyboard and mouse) are disconnected, and see if the problems persist. 
If you continue to have problems, then you'll likely have to boot the DVD installer dis and use Disk Utility to wipe the disk, and reinstall Mac OS X Snow Leopard onto the disk, and migrate your archive back in as part of the installation. 
If the problems persist after the reinstallation, then it's probably a hardware error with whichever Mac is involved here.  If this is a new Mac or under support, call Apple support and see what they have to say.  If you have a local Apple store, you'll check with the folks at the Genius Bar for assistance.

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