I recently got notified by the iPhone Things app with a message along the lines of "most people only rate the app when they delete it. If you're using Things, why not rate it right now?" and a button to go directly to the review page. I had no idea until I had clicked through that a textbox would be involved; I was expecting to just click on some stars and go back to my app.
Essentially you buy inventory from a specialized ad network, and they charge you by the install, using UDIDs to match the users who click on the ads with the users who installed the app. That way you get charged only for the users they actually sent you.
Most application ads convert poorly, so the companies doing the most volume in this space run 'incentivized' ads, where the user gets some virtual currency for installing the app.
For example, if they're playing 'Tap Widget', which normally charges for widgets, the user can get a widget for free by installing an application.
The user wants the widget, so they install the advertiser's application. The ad network sees the install and tells Tap Widget to give the user his widget. The advertiser gets a new user, so the ad network gets paid. The ad network takes their cut and passes the rest of the money on to Tap Widget. This works out pretty well for all parties.
I own a chunk of Flurry, one of the companies that specializes in this. There are others.
That said, I would love some organic in the App Store as well, but every scenario I can imagine to accomplish it, I can also imagine how to exploit.
Zero 'organic' is overstating it, but there definitely is a reason that there are terrible apps in the top paid lists.