There are so many news sites covering Asia, it all depends on what kind of news you're looking to read.
For starters, an easy way to find hot news is by using Google News. Not only do they aggregate all the top news articles for the day, it is also segmented by popularity and relevance.
For me personally I follow a few specific news sites covering Asia, and here are some of them:
1. Tech In Asia
As I'm passionate about startups and technology, I frequently read Tech In Asia's news since they have pretty good reporting and are fairly updated with what's going on in the region.
While they don't cover everything, you can get a pretty good idea about the big things that are happening out there.
2. News Asia Today
News Asia Today covers the latest lifestyle, technology, and some business news in Asia in English.
While their frequency of news isn't as high as some sites, they tend to cover news from a very simple and
3. Channel News Asia
Channel News Asia is a large and fairly awesome news portal that covers the latest news in Asia and Singapore.
I particularly like their topics covering startup companies as they are very insightful.
4. World of Buzz
World of Buzz generally covers news that are super hyped up / viral.
What I like about it is their writing style, which is very engaging and sometimes funny in a journalistic way.