If it was flattering for 37signals (read: influential company) to see this -- http://jasonzimdars.com/svn/ it will be even more flattering for not-yet-famous-company-X to see something similar.
1. pick a company that solves a problem that's interesting to you. or who's founder said something that resonated (in a talk, interview, or essay) 2. research their founding team 3. write / build / hand-craft / hand-deliver something (website, message in a bottle, anything, things non-digital like hand-written letters are particularly effective). 4. offer or do something unsolicited (logo, find a new customer, write effective copy for a campaign) 5. don't attach a resume. just write clearly, use nice paper, and expect nothing in return.
bonus: follow up if / when you don't hear back.
There is a line between irritating and hungry. You won't always be the latter but aim for it.
Do this 2 or 3 times, to companies that aren't yet big names (look through http://angel.co), and you'll floor their founding team with your level of effort and at least land an in-person.
Don't pick the job, pick the people and the problem. You'll find sufficient motivation later.