One of the simplest ways to go about this would just be to replace "<" with "&lt;", and ">" with "&gt;".

This way, you don't have to worry about balancing the tag beginnings and endings, and it won't break a message using the angle brackets to mean "less than" and "greater than".

Update: I probably got the idea from the forum at Joel On Software. Depending on how this is being used and your users, may also want to have a note telling the user that they can't use HTML to format their submission.

Another Update: Changed the second angle bracket to the closing angle bracket, changed the entities to match.