Using nmap

If not installed yet:
sudo apt-get install nmap

$ nmap sojourner.mayfirst.org

Starting Nmap 5.00 ( http://nmap.org ) at 2010-11-20 16:18 EST
Interesting ports on sojourner.mayfirst.org (209.234.253.110):
Not shown: 991 closed ports
PORT STATE SERVICE
22/tcp open ssh
25/tcp filtered smtp
80/tcp open http
110/tcp open pop3
143/tcp open imap
443/tcp open https
587/tcp open submission
993/tcp open imaps
995/tcp open pop3s

i have 9 open and 991 closed so i'm going to bet it tries 1-1000 :-)

stefan-agaric: with -p you can tell it the port range to scan.