Call a Bike
Now HERE is a fantastic concept. These bikes are to be found all over Berlin (and other German cities, apparently).
In Copenhagen we have City Bikes which can be rented on the shopping trolley concept - stick a coin in and get it back when you lock the bike.
But these Call-a-Bikes are a step up. You register and then you can call a toll-free number to be given a code to unlock a bike and it's yours until you don't need it anymore.
It's not free, you pay for it, but it's not that expensive.
Cool design, too, with that funky bag holder on the back.