You're looking for The Christian Science Monitor. Their whole reason for being is avoiding sensationalist reporting (biased reporting, I'd argue, is impossible to avoid completely). They go so far as to not use any of the wire services, so that biases don't creep in there, and use their own on-the-ground reporters instead.
What's tragic is that news sources like that are being plowed under along with the Fox Newses of the world with everyone's decision that "eh, blogs are just as good."
(edit: Well that's embarrassing. Apparently HTML markup doesn't work here.)
As far as sensationalism and lack of depth, I'm not sure they can really be faulted.
I use NPR as a counter-argument to saying that good content will find a way to make lots of money. Show me how because I don't see it.
Other than the Economist, I'm not aware of any news sources that have aimed for that type of trustworthiness as a selling point. I'd like to hear about any news sources everyone here trusts, not blindly trusts like my father-in-law trusts Fox News but empirically trustworthy fact-driven news.