You can try a target that you know has open ports, say your (personally owned or with express permission of the owner) router. Scanning without permission may be seen as a form of attack and can be illegal in some areas/situations.
$ nmap -sT [ip of router]
Starting Nmap 5.21 ( http://nmap.org ) at 2011-04-16 15:35 PDT
Nmap scan report for Service ([ip of router])
Host is up (0.023s latency).
Not shown: 997 closed ports
PORT STATE SERVICE
23/tcp open telnet
53/tcp open domain
80/tcp open http
Nmap done: 1 IP address (1 host up) scanned in 2.75 seconds
This will tell you if nmap is working properly.
for more information on nmap check out the man pages!