nmap is a program that scans all of the ports in your computer and sees whether they are open or not.
It cannot use them itself (but it can be used as part of a larger invasion to figure out how to exploit you).
What can YOU do about it ?
LEARN how to BETTER protect yourself !
The rule of thumbs for security is to have a multi-layered protection approach !
So do not use more than one virus scanner on active mode (it is OK to have one active and others in passive (manual scan) mode), one good cleaner, two or three Anti Adware/Spyware/Malware (they each detect something that the others have not seen) and one Email scanner (if your Virus scanner does not include one) but have at least one of each (for security).
You can only use one "software" Firewall (no options there as war between them will shut down your communication system if you have more than one) but, if you have a router, you can also activate its built-in Firewall as they use different methods.
Here are my suggestions for free (and paid) software you can mix and match to your liking according to the rule (I tried all personally at home and at work):
Anti-Malware/Spyware/Adware scanners suggestions:
Malwarebytes' Anti-Malware: http://www.download.com/Malwarebytes-Anti-Malware/3000-8022_4-10804572.html?part=dl-10804572&subj=dl&tag=button is a good choice and has gotten many people out of jams if you keep it updated.
Spybot: http://www.download.com/Spybot-Search-amp-Destroy/3000-8022_4-10122137.html?tag=mncol is also a good choice if you use it regularly and keep it updated.
Virus scanners suggestions:
Don't go for AVG free, it may be free but it has hiccups like the error that made the news late last year on CNET, it advised to remove a key component of Windows causing those who did to lose the use of their Windows system. The latest version of AVG pro (paid) is not much better.
Avast is good but takes a lot of resources in the computer.
If you need both Virus scanner and firewall, then the Comodo firewall http://www.personalfirewall.comodo.com/download_firewall.html is the top contender. If you want to pay, there is a pro version with extras !
Use it in combo mode (Antivirus/Firewall) at installation.
The firewall itself is very robust and the just-released version 3 includes a well-designed intrusion detection system and Vista compatibility. Comodo also supports internet connection sharing, whereas the free versions of Kerio and ZoneAlarm do not. Make sure that you install it in "Advanced" mode, because the "Basic" installation has the HIPS ( Host-based Intrusion-Prevention System ) disabled.
If you just want to use Comodo as a Firewall (or don't want a Firewall) then for Virus scanning, use Avira instead http://www.download.com/Avira-AntiVir-Personal-Free-Antivirus/3000-2239_4-10322935.html?cdlPid=10901492 It is very light on resources and the detection rate of viruses and rootkits is outstanding.
However, it does not include Email, Malware, Spyware or Adware scanners so complement by choosing from other suggestions on this page. Use the paid Avira pro (also light on resources) if you want these built-in !
Email scanner suggestions:
Spamdel: http://www.spamdel.com/
OR
Inbox: http://www.glenn.delahoy.com/software/files/Inbox.htm
Cleaner suggestion:
Glary Utilities: http://www.glaryutilities.com/gu.html to remove junk files or remnants of installs (there is always some).
Do not use Ccleaner ( In my time at helping others, I have found it more destructive than helpful and I had to rebuild systems nuked by it in the past ).
And of course, NEVER have them working scans at the same time.
When you scan, only the Firewall should be running alongside (in learn mode if need be).
Use a methodic "one after the other" kind of scan !
By doing so, you are on your way to being well protected BUT never relax your guard !