One of the best online newspaper designs I've seen recently is the Indian paper The Hindu (http://www.thehindu.com/). While most Indian newspapers will give you eye-cancer just by looking at them (ex: The Times of India, which is one of the oldest newspapers in the country also has one of the most horrible online editions, plastered with spammy ads and horrible layout). The Hindu has always been a bit of a boring (some might call it lack of sensationalism) but it's got an excellent new redesign. (The original design was like a 1995 webpage)
Also up there in my list is NPR (http://www.npr.org/) and PBS (http://www.pbs.org/). Not technically newspapers, but their pages are mostly about news delivery.
The Hindu looked bad too, a couple of years ago. They started testing a new interface at beta.thehindu.com for sometime before using the new interface for everyone.
The Hindu has always been a bit of a boring (some might call it lack of sensationalism) but it's got an excellent new redesign. True.
Also up there in my list is NPR (http://www.npr.org/) and PBS (http://www.pbs.org/). Not technically newspapers, but their pages are mostly about news delivery.