There's no central authority on this sort of thing, just a few sites scattered about here and there that try to keep a running list. The real problems come when a website is hacked, and instead of an obvious defacement, the perpetrator slips in a small bit of code to the website that causes it to try and install malware onto someone's system. It happened to the Bank of India not too long ago, and even more recently than that, some of Yahoo's ad servers were compromised in a similar way.
Probably the best thing you can do to help protect yourself against this sort of thing, is not use Internet Explorer. Regardless of all the various pet theories as to why it's such a popular target, it IS a popular target, so not being a part of the pool of potential victims is a good first step. Try out Firefox, Opera, and Safari... Keep 'em all, or just the one you like best, just be sure to pick one to be your permanent replacement for Internet Explorer. After that the only time you should ever be using IE is to download new security updates from Windows Update.
For various reasons, some other things you might want to consider adopting can be found in this list of suggestions I have for people in situations like yours. The more of them you follow, the fewer problems you will have.
1: Do not use Internet Explorer
1a: Replace it with your choice of Mozilla Firefox, Opera, Safari, or Seamonkey
2: Always install Windows security updates
2a: The lone exception to rule #1
2b: They're typically released every second Tuesday of the month
3: You should have some kind of firewall
3a: XP/Vista's firewall is good enough, routers are better, and third party firewalls are also viable options
4: Be sure to have an Anti-Virus program
4a: You can get AVG Free and Avast for free if money is an issue
5: Avoid pirated programs
6: Avoid file sharing (P2P) programs
7: Avoid using Outlook/Outlook Express
7a: Virtually any email program is safer, web email can be even better
I was on a website and a popup came on but there was no way to close it. the site winantivirus.com came up automaticly and would not let me close it I had to go to task manager and shut down explorer. So who can you report this to?