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.

Thank you thank you thank you! I thought I might have to uninstall and reinstall word b/c it was driving me CRAZY and it just started all of a sudden. I also googled for ‘backspace’ and ‘highlight’ and ‘microsoft’ and ‘word’ and yours was the first hit. Thank you!
Thanks. I am another beneficiary of your thoughtful gesture to post this information.
That’s a lot! that was puzzling me all the time
Had this problem (started suddenly) and searched google and your answer came right up. Thought I’d let you know your post didn’t go to waste. Thanks.
Thank you so much, worked a treat.