Good News starting today April 25, 2014. I typed in my serial number and I'm a candidate for a free repair.
If you have an iPhone 5 with a flaky power button, good news: Apple has just initiated an "iPhone 5 Sleep/Wake Button Replacement Program" that will replace your button, even if your phone's warranty has expired. The program begins today in the US and Canada, and it will launch on May 2 in other countries.
Enter your serial number on Apple's page to see if you're eligible for the program—if your phone has other damage (say, a cracked screen), that damage will first have to be fixed at your expense. If you're one of those holdouts running iOS 6, your phone will also be upgraded to iOS 7 as part of the repair.
If your phone is eligible, you can send it in by mail or bring it to an Apple store or to a service provider yourself. Repairs will take between four and six days, but 16GB loaner iPhones will be available for you to use while yours is being repaired, if you need one. My experience has been that most Apple stores will simply swap broken, in-warranty devices for working new or refurbished devices rather than repairing your specific unit, but the iPhone 5 has been out of production for several months at this point—Apple may not have enough left in circulation to replace all of the affected phones outright.
