Specifics, please, if a particular website, newspaper, magazine, etc.
npr
Asia Times Online is one of the best sources for in depth news from Asia. www.atimes.com The articles are far away from the fluff you get in western sources, they tell you who the players are and often have handy dandy maps of resource distributions.
Toronto Star, Globe and Mail, CBC, BBC, Sydney Morning Herald, CNN, Energy Bulletin, Bloomberg…
:: adds Asia Times to list ::
I like Drudge and FoxNews. I listen to talk radio most of the day at work, and they always break in when something happens (I first heard about the terrorist attacks on Sept 11 via a radio report.)
The Economist.
The SDMB, of course.
Besides that:
Ynet.co.il is my homepage. It’s the best Hebrew-language news site.
The New York Times website.
Slate.
I also read the weekend editions of Israel’s three major newspapers - Yediot, *Ma’ariv *and Haaretz - for more in-depth coverage.
BBC, Al Jazeera, MSNBC, The Pyongyang Times 
Boston Globe, World News Tonight, and BBC America – although I wish they’d switch to an Anchor Desk that didn’t look like a toilet.
For headline news, I listen to the radio every morning as I get up (News Radio WINS in NYC: “Give us 22 minutes, and we’ll give you the WORLD”).
I get actual in-depth coverage primarily through the NY Times and secondarily through the Wall St. Journal, online these days for the most part but I enjoy reading the printed paper at my in-laws’ or on an airplane/bus ride.
I usually also scan the NY Daily News and NY Post headlines online just to keep a finger on the pulse of the more salacious or local flavor news, and read the occasional article I find there that I hadn’t already seen or heard about via the radio, the Times or the Journal.
I also subscribe to the Economist, but that’s a weekly, so I usually don’t learn about events from it (as in, “I hadn’t heard about that”) so much as get a different, deeper analysis of them.
bloomberg is great.
BBC Radio 4 mainly. Sometimes Google News for eclecticism, sometimes the BBC News website.
On Sundays I often read the Sunday Times (UK, right wing) and the Observer (left), and if I do get papers during the week I get the Telegraph (right) and the Guardian (left).
Read an article recently praising the news coverage on Al-Jazeera because they didn’t simply cover stories to the extent they impact western interests.
For myself, it’s CNN.com for the morning headlines when I get to work, and Newsweek magazine for a bit more depth on the week’s stories. Sometimes nytimes.com, too.
NPR
NY Times
Washington Post
The Daily Show
The BBC World Service is similarly inclined - African, South American and Asian issues are given equal weighting to the regular western ones. Not surprising, therefore, that Al Jazeera grew from the defunct BBC World Arabic Service.
Fark.
Get the stories days to hours before the big dogs.
And then comment on it.
“Fark. We don’t make the news. We make fun of it.”
Radio: CBC, NPR.
Web: CBC, NPR as well. BBC. CNN.com is a joke nowadays. Local radio station has a short news page, and the local paper’s website (CFAX, Times Colonist). Also, a local Victoria forum is good for gossipy insider news before it makes the paper sometimes.
Television: CBC Newsworld (or whatever name they’re changing it to), CNN, CTV Newsnet. Local news and Vancouver news on the six or 11 p.m. news shows.
NYTimes
Washington Post
BBC World
NPR
Christian Science Monitor