:-/I would like to know if and how sites such as the search engine IXQUICK.COM and napster and other sites that DO NOT have advertising on them generate money.
A friend and I speculate that maybe Internet Service Providers pay them a certain amount of money for traffic that they generate, because if there were no sites of interest to any one there would be no reason for the Internet and Internet Service Providers to exist.

To be perfectly honest I don't know the answer to this question, however...

Working for an ISP I can tell you ow for a fact that we do not pay money to any of these companies. That would mean we were affiliated with illegal material and that would ultimately result in lawsuits among many other things. Just wanted to point out that ISPs don't keep file sharing companies in business.

Did you ever consider they are not out to make profit, but just want to share files? Not likely I know but it is possible. This way they would be able to get all of their servers and equipment paid for through "sponsoring" by people who also want to share files.

Up2us pays. I have several investments that create cash to pay those who join and surf

IXQuick does have ads on it, just not on the front page. When you do a search on a lot of websites you'll see something like "Sponsored Results". These results will always be at the very top of the list. This is one of the ways they make their money, companies pay them to have their listing at the top of a search.

Napster sells thousands of mp3's a day. They don't need to have advertisements on their sites as they make enough of a profit from their sales to pay their hosting costs etc. without the need to use advertisements.

Here are some other ways of generating income without the need for ads that I can think of:

Subscription Service
For example, DeviantArt. At DeviantArt you have a choice, surf with ads or pay a monthly subscription. If you pay the subscription you get a site with no ads along with other perks.

Asking for donation
A lot of sites have a PayPal button or something similar. They ask their visitors to donate to the site in order to help pay the hosting costs.

And that's all I can think of at the moment. Lunch time... *dashes off*