What happens when auto_increment on integer column reaches the max_value in databases?

Jim Martin’s comment from §3.6.9. “Using AUTO_INCREMENT” of the MySQL documentation:

Just in case there’s any question, the AUTO_INCREMENT field /DOES NOT WRAP/. Once you hit the limit for the field size, INSERTs generate an error. (As per Jeremy Cole)

A quick test with MySQL 5.1.45 results in an error of:

ERROR 1467 (HY000): Failed to read auto-increment value from storage engine

You could test for that error on insert and take appropriate action.