The truth is a hard thing to find these days so it’s probably wise to look at multiple sources. The Drudge Report is a good place to start. It’s a news aggregator which looks at all news agencies. The link titles are sometimes a little conservative-leaning, but drudge doesn’t write its own articles. USA today is slightly liberal. WSJ is slightly conservative. Fox is moderately right, CNN moderately left. MSNBC and Huffington Post are only worth looking at to see what the crazies are saying and Rush Limbaugh is way right but if you want to stay well informed, you’ll need to listen to him too.
For certain, very large values of “moderately”. 
I too enjoy the Christian Science Monitor, and I’m a big fat atheist.
Christian Science Monitor, yes, but also the Wall Street Journal. I have an iPad subscription and it’s great, very convenient. Fair and balanced, too.
Give this American the BBC. At least they’re free from the American political influence.
Oh yeah, and Fox in America. They claim to be Fair And Balanced. They couldn’t claim that if it weren’t true, right.
In addition to the other recommendations, I’m told that Russia Today is good for international news. I’m a bit dubious of this, as it’s Russian state news–but it’s another perspective, at least.
What, no mention of the CBC? 
(The quote refers to The Christian Science Monitor.)
Yeah what’s up with that? The CSM has a well-earned reputation for solid, quality, unbiased reporting. If one didn’t know better, a paper published by a slightly nutty religious sect would seem to be a bunch of dogmatic foolishness. And yet it’s not. More power to them.
The CBC is pretty good stuff too.
If you live anywhere along the northern side of the country, you can surely pick up the news from Canada. All the way back to Nixon impeachment, I alternated between NPR and CBC…and like both. Of course, back then, ABC, NBC, CBS all had excellent news gathering organizations and did not ever seem, to me, to be leaning one way or t’other.
I’ve never quite understood Canadian politics, West vs. East, Quebec vs. the rest, etc. but when they report on doings in the rest of the world, they seem to me to be absolutely unbiased and well informed.
Counterpunch says it Tells the Facts, Names the Names. As a source for independent journalism they do not suck up to the major parties. Generally they are disdainful of the actions of both sides of politics. However they would be considered socialists and are thus probably too scary to read but they do provide another view of what is going on.
From a world news perspective the CBC isn’t too bad, but internally it’s slightly left-wing biased. Again, not too bad but noticeable. I think CTV is more balanced all around.
Despite being regarded as a newspaper whose readership is typically thought of as soap dodging sandal wearers who who would equate the Morning Star with The Daily Mail, and some columnists who put the “Bleeding Heart” into liberal, IMHO The Guardianis a fairly balanced source for news.
Christian Science Monitor is only tentatively involved with the Christian Science sect, and has been that way for many years. The name and a religious column are contractual obligations, much like ABC Family being required to have family in the name and showing 700 Club. Christian Science Monitor has an excellent reputation for news and has won many awards for its reporting. They are a good example of what news reporting should be- very straightforward and not sensationalistic.
If you’re in the US and looking for an unbiased source, the best bet IMO will be NPR. I watch a lot of MSNBC but I’m fully aware of its center-left leanings (I’m liberal as Hell but not even I agree with everything that Rachel Maddow or Lawrence O-Donnell has to say); still, MSNBC does have a decent amount of relatively “unbiased” programming in its early morning shows with stuff like* Morning Joe* or The Daily Rundown.
Every now and then I’ll turn on Fox News for shits and giggles, but the garbage that spews out of the talking heads on that network is so far-right that I can only ever make it a few minutes before I have to change the channel. If you’re looking for unbiased network stuff, then I guess CNN is probably the closest you’ll find, but even I think that that channel is center-right.
On the internet I generally alternate between Huffpo and Politico; of those, Politico is the least biased, but it still has a noticeable right-leaning slant to it. If you want a bit of everything, RealClearPolitics does a decent job of assembling a bunch of stuff from a variety of online sources within the political sphere.
I’d believe the reporting from Weekly World News before watching MSNBC. CSM is moderately neutral and trustworthy. But romeo2die is pretty much correct. Don’t trust the political news from the home teams. Go to the people on the outside for objective reporting. They generally are more clear headed.
There’s is Democracy Now! which can be accessed on a lot of media markets: http://en.wikipedia.org/wiki/Democracy_Now
They’ve run articles from Fidel Castro in the past. Just sayin’.
I’d say the Washington Post is the most centrist of the national newspapers and Atlantic among the newsmagazines although the New York Times isn’t usually too flaming liberal either, although the comment’s section is a different story.
I don’t trust any single site. So my reading habits are pretty eclectic -
Left and right
Local, national and global
Black, white and Hispanic
Religious and non-religious
What happens is less important to me than people’s reactions to it. And that isn’t a factual issue. So once I can reasonably ascertain the facts of a news event I am more interested in different groups of people’s responses based on how it affects them.
Most of the mainstream US media (i.e., non cable news) work hard to avoid bias. Places like the AP, Yahoo News, NBC, ABC, & CBS all strive to be unbiased and accurate (though, of course, there are minor errors and biases everywhere).
The myth that the mainstream media is biased is because the don’t always report what’s important to a small minority but no one else, or they report things facts that are embarrassing to your political viewpoint.
English-written Russian news site. They cover a lot of stuff US media outlets pass on, and it’s pretty much entirely unslanted facts, as they have no reason to be biased.