On their status log Twitter acknowledged that they are having system issues:
“We are currently experiencing site stability issues. There may be intermittent issues loading twitter.com. We’re working to fix it as soon as possible.”
While Twitter is valued as a multi-billion dollar business they have a long history of running as if their service was being operated out of someone’s basement on a Commodore 64, recently they promised that a move to their own dedicated data center will solve their issues, hopefully that move arrives soon.
At this time the reason(s) for the system wide shutdown are not known.
Update: It looks like the site is back up and running for the time being.