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.

You saved my life with this–I was pulling my hair out, and wasn’t going to make it much longer!
Thanks! Thought it was the new keyboard!
Not that I don’t love the del key…but this backspace thing was really starting to get to me. Thanks for alleviating frustrations. Now…to figure out how that box got unchecked….
Thanx Mate, it worked
I had to struggle writing so many assignments with this problem! Now I can relax, thanks!!! 
thnx for the solution!!~
i was going crazy XD