Audit logins on MySQL database
You would probably want to use the general query log. 


  The general query log is a general
  record of what mysqld is doing. The
  server writes information to this log
  when clients connect or disconnect,
  and it logs each SQL statement
  received from clients.


One important thing with logging for security is that an attacker cannot access the log to erase traces of their presence, so consider append-only files. 

FWIW in Oracle we can send logs automatically to a remote syslog, but I don't believe MySQL has this feature yet. Perhaps you could fake it with SNMP but I have not tried it.