I really need to know if the virtual games that my children like to play off the internet is letting viruses and spyware in on my system. Some of the sites they like to play are; Howrse, Neopets, Spore, Warriors and Travian. There may be a couple more, but I just can't think of them at the moment. I also need to know if they are letting pop-up ads through.

I doubt you will have any problems with virus's for those games. Do you run any anti-virus software?

Get a good anti-virus, and internet protection, which will take the job to trace for viruses and remove those and warn you regarding the viruses from the sites...
Whatever may be the site, anti-virus and anti-spammer's will remove any viruses from the PC.

It is best to install anti-virus softwares in PC's. When you browse any site it will display you the security warning regarding any viruses detected in that particular site. If it contains any type of viruses then it detects those viruses and removes them. Then there will not be any problem for your computer. So, first it is better to install anti-virus softwares first. You can download these softwares from internet directly. You have the licensed and non-licensed versions. It is better to download the licensed versions.