If you have been trying to log in since around 12:00 EST, then you are probably not having much success. There is currently no word from Twitter on the outage. Stay tuned for any updates!
13:15 NYC time UPDATE: Twitter.com service seems to be fully restored. We shall never forget where we were the day Twitter.com went dark... for an hour. Note that Twitter may go down in other parts of the world over the next hour but should be back up within an hour.
13:08 NYC time UPDATE: Aaaand... Twitter.com seems to be back up. Still some delays in tweeting.
12:53 NYC time UPDATE: Log in via https://mobile.twitter.com/ to continue to Tweet during this outage.
12:49 NYC Time UPDATE: Twitter has acknowledged the downtime and posted:
Users may be experiencing issues accessing Twitter. Our engineers are currently working to resolve the issue.