Salon & Slate come to mind.
Relatedly, Politico, a US politics site, makes a lot of money from its print edition - http://en.wikipedia.org/wiki/Politico#Distribution_and_conte...
Granted people don't normally go their for "news" but it keeps up with major news stories like earthquakes, the Olympics and other sporting events, economic issues etc.
http://en.wikipedia.org/wiki/Financial_crisis_of_2007%E2%80%... (ongoing) http://en.wikipedia.org/wiki/2010_Haiti_earthquake (recent) http://en.wikipedia.org/wiki/2012_Summer_Olympics (future)
I subscribe to The Economist and New Scientist, as reading them online just isn't very user friendly. With the Economist and New Scientist I get full access to the archive and the online edition when I subscribe, but I don't want only the online edition, it is a hard reading experience compared to the magazine. Will the iPad change that? Time will tell.
I have recently dropped my newspaper subscription, which I actually miss. Their website is good, but not at all a replacement for the paper edition. The content is structured differently and more importantly, hard to browse quickly. Wherea the newspaper is very good to allow me to quickly get an overview of what is going on. But I dropped it as an experiment because I don't read it enough and I get a ton of paper to recycle.
I am looking forward to news delivered to me electronically in a way I will consume as willingly as printed news. The web as it looks today is not it.