[schipplock]

I use "nmap" for this.

  $ nmap example.com
  PORT     STATE  SERVICE
  80/tcp   open   http
  443/tcp  open   https
  1119/tcp closed bnetgame
  1935/tcp closed rtmp

[exciteabletom]

A more complete answer using nmap and cron:

    MAILTO="[e-mail]"
    */30 * * * * nmap yourdomain.com | grep open > nmap.log.tmp; diff nmap.log nmap.log.tmp; mv nmap.log.tmp nmap.log