The sites that are still up for Kazaa and all of its incarnations are all mirror sites. Kazaa itself is run from outside the US and the US has not legal juridiction in Vanuatu, a small island country in the south Pacific where Sharman Networks is located. And when you use the Kazaa software, you are not connecting to a website, you are connecting to sometimes hundred of thousands of other computers. When you are online and connected to the internet, what ever you have in the "My Shared Files" folder is available to anyone else using Kazaa. Kazaa itself in actually old networking software packaged with a basic web browser and MP3 playback software. Having Kazaa on your computer itself is not going to get you in trouble, there are legitimate reasons for using it. I have used Kazaa quite a bit myself, it was a handy way for me to make certain files available to others without sending large emails. If you are just a downloader and use Kazaa reasonably, there is no reason to worry about anything, the RIAA is not looking for those folks. There are others that have set up large servers with large amounts of illegal files and they make them available to Kazaa users. Some honestly believe that it is fair to share music on the net, others do it out of spite. These are the people the RIAA are looking for.
BTW, the only reason I remove Kazaa was to remove the temptation. I too found the world of P2P networking to be highly rewarding.