First, my background:

• I'm in the market for a new job
• I have ~2 years experience under my belt
• Nothing on my resume would JUMP out at you
• Thus far in my career I've been able to become productive quickly and have been continually praised by managers and coworkers for my abilities to learn and produce. I don't mean to be bragging here, but I want to get across that (at least in my mind) I could be categorized as "very promising young developer"

I've been job hunting for a little while now and like most job seekers I've found a handful of companies that are basically "dream" jobs (think Fog Creek or 37Signals). If I were to apply to a company like that in the normal recruitment channels, my resume would probably not make it past the first set of filters.

Now, I accept that I'm a longshot for a job at the hottest companies out there, but in my job search I've had a little success in applying for positions I'm not qualified for simply by doing something a little different: sending an email outlining how I don't meet the qualifications but stating why I would do well in the job anyways. In other cases, I've outright asked for a small project/problem that would be representative of the work to prove I can do the job, since I didn't have the specific skills on my resume yet.

What I'm wondering is: If I'm not qualified on paper for a particular job, what creative/unique/impressive methods have you thought of or seen work to at least get an interview?

For the sake of argument, assume I really am a "very promising young developer". I would love to hear from people who are responsible for hiring - I'd like to hear examples of techniques that got someone noticed when they otherwise wouldn't have.

Clarification: I know that I need to continue building my resume to continue advancing. But I'm in the job search NOW, so I'm looking for other approaches