Ads and the API: Illegal or Allowed?

What is the policy on ads appearing on/in applications/websites/etc. that make use of the API? I was under the assumption that they weren't allowed and was preparing to try and scrub my service clean of any ads that might appear, but I've come across various applications that both use the API and have ads. I don't know if those applications are technically in the wrong or not, and as such I wanted to get this straight before I spend a large amount of time doing this in case it's not super necessary.