Can Google ranking be bought?

This came up from a conversation with a friend.

He was very certain that any one website owner can pay to have their website rank higher in Google. I am not talking about Google AdWords on the right hand side, or the highlighted sponsored links on the top of the page.

I need clarification on this. As I always thought that Google ranking is based on many other factors, such as site content, quality of links, length of stay for each click, etc. but not for how much the website owner has paid Google.