My roommate just had this problem with Microsoft Word 2003, and I found the fix using the Google search engine. Here’s what you do:
Tools -> Options -> Edit
Check “Typing Replaces Selection”
That’s all my roommate had to do. For the sake of completeness, the fix also says:
Tools -> Options -> General
Uncheck both options that have WordPerfect in them
Hope this helps someone.

Thanks heaps for this. It was literaly driving me UP the wall!
Thanks again
Thanks so much! I have no idea how that box got unchecked but it’s been driving me insane for days! You are wonderful.
THANKS SOOOO MUCH
Dude, thank you so much. I use backspace so much when I want to delete my text and when this problem occurred I was so conscientious of that. It’s so much easier for me to just backspace text than highlighting and pressing the delete key. Unlike random blogs that had complicated and superfluous instructions this was very straight forward. Thank you!
Yes!!! I don’t have to destroy my computer after all!! I tried to ignore it but insanity was taking over. So I googled it and this savior blog popped up and, lllaaah!! (shining light onto monitor)