I agree with Jeff about USA Today, NY Times and Weather Channel apps.
I prefer Thomson Reuters “News Pro” (free) to “AP Mobile” which I still have but will probably delete from my Touch. The Reuters app just runs a bit better and I pretty much get the same news.
http://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=314213167
I also have ‘WSJ’ - the free Wall St. Journal app, which does 2 cool things: first, it gives you everything from allthingsd.com (which the Journal owns) so you don’t need the separate allthingsD app, and second, it pierces the pay-wall the WSJ has and lets you read articles for free that you’d have to pay for via membership if you went to wsj.com with a browser.
http://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=311822183
The Huffington Post does nice news aggregation and blogs from everything from breaking news to politics to comedy to arts:
http://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=306621789
For British news, The Telegraph out of the UK has its own free app:
http://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=303301873
NewsDesk offers aggregation of major stories from UK sources and elsewhere (NYTimes, BBC News, Aljazeera, Reuters, CNN), but when you click on a headline it sends you into a minibrowser to read the article and doesn’t look at good as something like the NY Times app:
http://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=292301139
News UK Lite is a free version of an app which aggregates the top stories from major British news sources (BBC News, Telegraph UK, UK Guardian) and allows for some customization:
http://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=292181641
The company which produced News UK Lite has similar versions available for download: News Canada Lite & News Australia Lite. I just noticed they have a USA version that aggregates top stories from your choice of CNN, USA Today, MSNBC, BBC News, Fox News, Bloomberg, LATimes, CNET, MSN Money and others. Nice! Unfortunately the iTunes Store keeps giving me an error when I try to download it!