From Google: "Apps and their ads must not add homescreen shortcuts, browser bookmarks, or icons on the user's device as a service to third parties or for advertising purposes. Apps and their ads must not display advertisements through system level notifications on the user's device, unless the notifications derive from an integral feature provided by the installed app. (e.g., an airline app that notifies users of special deals, or a game that notifies users of in-game promotions)."
The Google Search app will be able to show Google Now ads for nearby businesses, but a random game won't be able to show ads for third-party services.
There are a lot of Android apps like TrustGo Ad Detector or Lookout Ad Network Detector that show warnings if you install apps that use ad services like AirPush. "Smartphone usage has skyrocketed, and some advertisers have begun to experiment with aggressive, new techniques to display ads on mobile devices. This includes pushing ads to the standard Android notification bar, dropping generically designed icons on the mobile desktop, and modifying browser settings like bookmarks or the default homepage," explains Lookout.