The obvious answer is "advertising" but I've heard of a lot of decently popular sites that don't make much on advertising. How else do you make money? are they just hoping to get bought out?
And for those who do have a "premium" service, how many customers actually pay for it?
EDIT Thank you guys for you answers. I'd like to emphasize the second part of this question, how hard is it to get users to sign up for the paid version of a website when you have a free one? An example I'm thinking of is Tripit. I use it, but I use the free version, and I don't really see a reason to sign up for the paid one...
On the other hand, I use freshbooks, and did pay, because I needed more than 3 accounts.
The person who pays the bills IS the customer.
NO company makes money by not charging the customer. They may have a business model which makes money by not charging a user of their services -- but they do not make money by not charging their customer.
A start-up that fails to understand who their customer is will be in trouble.
If you are providing a free service to users and are selling advertising -- then the customer is the advertiser who is buying access to your user base.
There are lots of different types of websites. They do not all have a business goal of making money. Some are marketing sites and their value is part of overall marketing campaigns and initiatives. Some are hobbies. Some see the payoff they will get selling equity to a VC after they have a bazillion users -- the customer is the VC. Some hope that a business model emerges at some point in the future if they just get enough people to their site.
But for those of us building sustainable business models that deliver product/services to customers we always need to stay focused on the definition of customer as the person who pays the bills -- whether on a website or at the lemonade stand.
There are quite a few honest and not so honest ways for a company to make money without charging customers directly.
One thing to keep in mind that sometimes a site won't need to make any money as long as it doesn't lose too much. This is very true for side projects of larger enterprises that simply increase the awareness of a brand or company. Think about the Coca-Cola website, or the Nike website. They have no direct sales but in aggregate increase brand awareness.
Hope this clears things up a bit.