Non-Linux FOSS: Angry IP
The de facto standard for port scanning always has been the venerable Nmap program. The command-line tool is indeed very powerful, but I've only ever seen it work with Linux, and every time I use it, I need to read the man page to figure out the command flags.
Windows users have been able to use the "Angry IP Scanner" tool for quite some time, and recently, the program (since version 3) has become truly cross-platform. If you need to scan for open ports on a specific host or on an entire network, the Angry IP Scanner (or just ipscan) tool is fast, robust and, of course, open source.
Grab a copy of this awesome little FOSS tool from its Web site at http://www.angryip.org or directly from SourceForge at http://ipscan.sf.net. Just remember, port scanning is one of those skills that can be used for good or evil—be sure you're wearing your white hat!