There has been a lot of discussion around the Google Farmer Update that ads play a role.
Meaning, if you have too many ads, Google might look at that as a sign of low quality content and drop your rankings for the site overall.
Vanessa Fox mentioned it as well in her lessons learned article saying:
Matt said that having advertising on your site does not inherently reduce its quality. However, it is possible to overdo it. I had noted in my earlier articles about this change that in particular, no content and only ads above the fold, as well as pages that have so many ads, it's difficult to find the non-advertising content often provide a poor user experience.
That being said, Google's JohnMu just commented on it in a Google Webmaster Help thread saying:
Another factor that Lysis mentions is ads. For our algorithms, ads generally don't play a big role. However, they can play a role with your visitors.
Forget the user side, did John say in Google's algorithms ads "don't play a big role." Do they play a small role? Is it about the content to ad ratio? Or is he implying that sites with lots of ads typically have low quality content? There are so many ways to read it. Probably the best way to read it is how Vanessa put it above.
Forum discussion at Google Webmaster Help.