New York Times
Newspaper: http://www.nytimes.com
Conservatives accuse it (along with most other newspapers) for being too left-wing, but represents probably the most important newspaper in the country. Also interesting for its Op-Eds, though many of those are pay-only. All other articles are available with free subscription. 

Wall Street Journal
Newspaper: http://online.wsj.com/public/us
Covers primarily the financial sector of the news. Scan the What's News section. (Most articles are unfortunately pay-only, though they offer a free 2-week trial) 

The Onion
Newspaper: http://www.theonion.com/
Mock news source. Spoofs American news stories and particularly cultural references to American life while maintaining a journalistic style. 

CNN
Online journal and TV: http://www.cnn.com/
Fairly straight-forward news source.  Scan headlines for a relatively comprehensive view of what today's issues are.  Articles tend to be less extensively presented and researched than at the New York Times or the Wall Street Journal.  Also includes populist American news (i.e. Britney and Kevin file for divorce.)

Fox News
TV: http://www.foxnews.com/
Essentially the voice of right-wing America.  Look under Video then Shows for such videos as Bill O'Reilly's blunt, Conservative opinions on American policy and social issues.

Comedy Central's The Daily Show
TV: http://www.comedycentral.com/tv_shows/thedailyshowwithjonstewart/
Part mock news show, part late-night interview style. Jon Stewart leads the show by drawing comedy from political and national news, consistently poking fun at the way political actions are presented and at the way news is broadcast in the US.

For information, the first stop would have to be the ABC at www.abc.net.au. They have a huge selection of video on demand, ranging from news and current affairs to comedy and music video programs.
The video on demand site is http://www.abc.net.au/vod.
The news and current affairs page (http://www.abc.net.au/vod/news/) has 1 minute news bulletin and a longer 10-15 minute broadcast which can be watched in flash player on the site. They're also updated several times a day.

For beginning or intermediate students, 'Behind the News' could be quite useful. In Australia it's usually shown in upper primary and lower secondary school, and treats current events in a simplified manner. Some students might find it over-simplified, but the language level is certainly simpler.
The website is http://www.abc.net.au/tv/btn.

For listening material, often with transcripts, there's a huge range at ABC radio: http://www.abc.net.au/radio. You can listen live on the internet or download recent past programs.  Only recent broadcasts are available in audio format, but there is an extensive archive of transcripts and program summaries.

Otherwise, all the major Australian newspapers have useful websites, with both the current issue, up-to-the-minute breaking news, and a free archive covering several weeks.  They are:

• The Australian www.theaustralian.news.com.au
• The Sydney Morning Herald www.smh.com.au
• The Age www.theage.com.au
• The Courier Mail www.news.com.au/couriermail/
• The Daily Telegraph www.news.com.au/dailytelegraph/
• The Bulletin (magazine) http://bulletin.ninemsn.com.au
  

The first three are the most reputable.  Some websites have short video clips in addition to the normal newspaper sections.

Finally, as regards cultural sites, the ABC again tops the list, with many cultural TV and radio programs. The arts TV video on demand site is http://www.abc.net.au/vod/arts.

For radio, Radio National has a lot of cultural programs: http://www.abc.net.au/rn/programs.

The indigenous affairs website on ABC is http://www.abc.net.au/message  - for articles, audio and video on indigenous topics.

For general Australian civilisation, etc. at a simplified language level, there's the education website, http://www.abc.net.au/learn/schools/.

For American culture, and information as well, CNN and the New York Times have educational websites: http://www.cnn.com/EDUCATION/ and  http://www.nytimes.com/learning/index.html.