My regular news sources are below. I check multiple times per day, and get email notifications of breaking stories from three or four different places.

The New York Times - Breaking News, World News & Multimedia
BBC News - Home
AJE - Al Jazeera English
Business & Financial News, Breaking US & International News | Reuters.com
RealClearPolitics - Opinion, News, Analysis, Videos and Polls
RSOE EDIS

Also we have the TV news on 24/7 unless someone wants to watch something else. It varies between BBC, Channel 4 News, CNN, and occasionally Sky News (Though my mom hates it so that's rare).

Oh, and if something big is going down, I'll essentially go to any news site I can think of, even if I have to muddle through Google's attempt to translate Yupik into English.