United had to ground all of its mainline flights nationwide around 7:40 am Eastern today due to the failure of a computer system.
UPDATE: 10:05am Eastern. The ground stop was lifted (14:00 UTC).
United has issued a statement:

"We experienced a network connectivity issue this morning. We are working to resolve this and apologize to our customers for any inconvenience."
Reports conflicted on the exact problem. The Federal Aviation Administration blamed a "traffic management system".
United's passenger service system (PSS) is in-house, adapted from merger partner Continental's. It's SHARES, renamed HP Passenger Service Solutions when HP bought it. It's unclear if the PSS is the problem, though.
Ground crews were hand-writing boarding passes. Journalist Joe Brancatelli, who is posting real-time advice for stranded business travelers, said:

"If you are checking in online, you will apparently get a boarding pass via e-mail (at least you were able to several minutes ago), but no flights are moving, so, you know, zero sum."
In the last month, United has cancelled about 1,700 flights and issued 20,200 delays, many around June 2. That's four times the number that Delta cancelled and double what American Airlines canceled.
United's on-time performance in June was estimated at 65%, down from 77% in May. July could be worse it seems. United's commuter carriers are also suffering.
UPDATING, as information becomes available.
NB: Image courtesy of AgCommunicator