I believe there is no one Web site which can be considered the best. But if we talk through the categories, it would be more reasonable. Each selection of news sites will be a subjective choice of course.
Best Political News Site
I would say the international edition of the Guardian is the best in this category. They are truly objective and they did a great job with Snowden files.
Top Sports News Site
I would go to Bleacher Report because they not only provide detailed news, but they also offer a great pre-match analysis.
Best Humor Site News
As a person who has a special interest in Turkey, I would say BizarreTurkey.com. They publish real news that is absolutely crazy. Definitely worth having a look to understand the Middle East.
Top Tech News Site
Techcrunch because they not only provide great technology news but they organize events that are very important as well.
Best Finance Site News
For obvious reasons, the Financial Times.