Old fashioned, I know, but I listen to the radio. I often have BBC Radio 4 on in the background, where I can catch the hourly news. Then there' she excellent Today program in the morning and PM in the afternoon.
I'm a big fan of the BBC World Service, which tends to have more content and less human interest compared to Radio 4. In particular 'Newshour' is the best general world news coverage I've found, and available as podcast http://www.bbc.co.uk/podcasts/series/newshour
and there's Democracy Now -- it's unashamedly politically biased, but brings up important stories that don't get covered much elsewhere. The best part is the news roundup at the start -- the rest is features and interviews, which can be very good or entirely dull. http://www.democracynow.org/podcasting
Doesn't sound too old-fashioned to me, given the popularity of online radio. Still, I'm not sure I'd be able to focus on stuff if I had radio on all the time.