Google is known for its non-tolerance for paid links to a site. Previously, sites tended to gain ranking on account of the paid links they had pointing to themselves. Bu Google has been working on its algorithm, and the Panda and Penguin updates have been all about cutting down on such spam activities. Now Google delivers a penalty to such a website that has paid back-links. But if you come to think about it, don't ads seem to do the same thing? For example, if you buy an ad slot on a website that points to your own site, then how is that different from links on other websites that you buy?
Google is not against advertising. It is great for educating people, and alerting them. It can drive traffic to a site, and raise awareness. And there can be a lot many reasons for advertising, but Google has nothing against them.
But the simple answer to the question is, one type on link manipulates search engines, whereas the other type does not (you can guess which does which). When you're paying for links that pass PageRank, fundamentally, you are paying for something that manipulates search engines, something that creates the worst search experience for users, and hence violate Google's Terms of Service.
So you can use AdSense, DoubleClick, Chitika, or whatever you're interested in. What Google looks for is, whether search engines get worse, or whether PageRank is being passed, and whether search engines get manipulated by a particular set of links.
So if you have a link to your site that passed PageRank, then that will definitely harm your website more than it will do good. If you're doing advertisements just make sure those links don't pass PageRank and manipulate search engines in any way. Avoid spamming :)