Being a San Francisco renter myself, I feel your pain. It's much the same situation here.
If you have a smartphone, I'd recommend using our Trulia Rental app, as it was specifically designed to help renters in swift-moving, usually urban areas.
You can create a search alert with the app, which will push an alert to you the moment a new property fitting your criteria is posted on Trulia. Also, because the alert is pushed to your phone, you can call right away and be amongst the first people to call the property manager, making your chances of finding a pad that much better.
Here is a link to our iPhone and Android apps:http://www.trulia.com/mobile/iphonerental/
You can also do searches on our website, but that won't have the same push alert feature that going through our app has.
I hope that helps, and from one renter to another, I wish you the best of luck!
My wife and I moved here in 1990 and ran into the same situation you are encountering. After wasting our time competing with everyone else we started asking people we ran into while walking around. It did not take long and we found a sweet old lady working out on her front porch who had 2 empty units upstairs in a big old house in Irvington. 2 years later she financed the purchase of our first home. 20 years later she financed our purchase of a duplex in Willamette Heights and wrote us into her will. Be nice, be responsible, be helpful and be ethical because it will be to every ones benefit. Good luck and happy hunting.
I have found that going through more localized searches can be benificial when looking for a rental. I know The Oreginian has thier marketplace online classifieds. I know how hard it can be when by the time you call on that craigslist ad thier phone has already been blowing up.
Look for "outside of the box" places to search as well post what you are looking for. I think the internet is wtill great for finding places to rent but dont forget to look for better ways to find the new listings before they hit craiglist. I use facebook groups, online local newspaper and college websites, and good old fasion fliers on corkboards to name a few.
Good luck and happy hunting!
I have heard of several people confronting this issue who have been, in a way, forced to purchase b/c they are unable to find a rental unit-let alone an affordable rental unit.