There was a short period in the financial crisis where T bills had negative yields on the secondary market. They weren't issued that way, but there was such a flight to safety that people were paying more for them than they were going to get back.
So yes, negative yields are possible. They normally happen during a flight to safety. Would you rather risk losing all your money, or pay someone 1% to guarantee its safety? We don't need to worry about that. But if you had money in Greek banks? Oh yea... it might be worth paying the Swiss or Germans to keep your money safe.
There is also the concern about deflation. Inflation is bad for bonds, but deflation is good for them. Deflation just so happens to be bad for everything else. By pushing yields negative they are forcing people to move out of safe assets and either into equities or into spending the money. These should help prevent deflation.