Personally, my all-time favourite is The Economist (which contrarily to what its name suggest is not just about the economy). It is the best written and most interesting news source I have come across. The drawback is that it is only published once a week.

In second place would be BBC News for quick updates on the daily news and some relaxing "trivia articles".

In third place, I'd choose the Japan Times as it's currently the best English-language news site about Japan (Mainichi is too tabloid, Yomiuri is a bit boring, Asahi is good but doesn't have enough articles, and Kyodo is too concise).

NB : the purpose of this thread is not just to share opinions, but hopefully to discover some good websites in the immensity of the WWW.