How to gain webapp exposure from a generation notorious for hating advertising?

In building web applications, I keep running up against an issue: How do I gain exposure without pissing people off by telling them about my product?<p>Users are numb to advertising. Scoping Twitter updates for potential users looking for a solution you offer seems wasteful, and a bit creepy, and seems like the wrong context to reach out to users. Being featured on sites that deal in what your web app offers seems like a shot in the dark at best.<p>I don't want to shove apps down people's throats. I want them to want to use it. How does one go about that?