Are the popups the same ones and along the lines of a trial period has expired and / or you are required to pay a subscription. OR is it a popup that can't be closed and you have to let it run it's course before being able to close it. If the answer is yes to any of these then go straight to PART 2.
<<< PART 1 >>>
It could be caused by a number of different things - it may be adware in it's normal sense, it could be malware of it could be being caused by a program which has become installed on your computer.
Adware causes unwanted ads to appear, sometimes this is the price you pay for using free software, other times it's completely unwarranted.
Spyware is software on your computer that spies on you - which websites you go to, which programs you use and in some cases reports back on your every move including sensitive data you may key into your computer (passwords, credit card details etc).
Malware is a generic term for 'bad programs', things like viruses and worms. These can do pretty much whatever the writer has programed them to do, they may be relatively harmless or may corrupt your entire computer.
More about adware, spyware etc from Microsoft...
http://www.microsoft.com/windows/ie/community/columns/adware.mspx
http://www.microsoft.com/athome/security/protect/windowsxpsp2/Default.mspx
Google Pack is an excellent set of programs which includes 6 months free subscription to Norton Anti-Virus as well as adware and spyware removal programs. There's loads of other stuff like the Google video player, Google Earth etc... http://pack.google.com
Free Anti Virus Software:
AVG - http://free.grisoft.com/doc/2/lng/us/tpl/v5
Avast - http://www.avast.com/eng/avast_4_home.html
Clamwin - http://www.clamwin.com/
Free Adware and Spyware Removal Software:
Windows Defender - http://www.microsoft.com/athome/security/spyware/software/default.mspx
Lavasoft Adaware - http://www.lavasoftusa.com/default.shtml.en
Spybot - http://www.safer-networking.org/
AVG - http://free.grisoft.com/doc/20/lng/us/tpl/v5
Try installing some of the above and see if that gets rid of the problem - hopefully it will. If not then continue on to part 2.
<<< PART 2 >>>
It seems probable that you have a program installed which is causing the pop-ups. The program won't be adware, spyware or a virus so it's unlikely to be detected by security software. If this is the case then you need specific instructions for the manual removal of the program and files and this can sometimes be a long winded and tricky business.
If the pop ups are for a particular product or service then try Googling the product name - this may lead you to removal instructions.
Another option is to perform a system restore - this will take your computer back to a previous state. There's more info and full instructions on this page... http://www.microsoft.com/windowsxp/using/helpandsupport/learnmore/systemrestore.mspx
If nothing works then post another question and include as much info as poss about the adverts - what they're for, what site they link to, are they random or every time you perform a certain action etc etc.