I can do all of that. And I can do it all really well. I don't normally toot my own horn, but this all just seems like part of the job. These are skills that I've acquired over 13 years (I'm only 23), and apparently the combination is more desirable/rare than I thought.
Here's the thing, though: I don't consider myself a 'designer'. I think the title is too limiting, because it doesn't encompass other skills (like coding). And while I would never call myself a 'designer', I could probably outperform 99% of the designers I've come across.
Some recent work:
http://grubwithus.com (if anything is ugly/weird here, we're heavily A/B testing right now)
http://itunes.apple.com/us/app/grubwithus/id492155022?mt=8
http://techcrunch.com/2012/01/11/grubwithus-goes-mobile-with...