As you do not mention having a mouse (?) perhaps you are lightly brushing the touchpad with your wrist or a loose blouse/shirt sleeve as you type? This can easily happen with laptops. If you use a mouse you can disable the touchpad to avoid this.

I have tried using a mouse it does the same thing with a mouse plugged in and the touch pad disabled. You can be typing and cusor will move and place letter in sentences already typed.

Did you try:

The basic reboot?

A System Restore back to a good date?

Booting up in Safe Mode to see if the malady still occurs?

I don't really think this is it, but years ago there was reoccurring malware which effected cursor movement. When all else fails a couple good scans can't hurt anything.

DA