In general, streaming audio and video on the Touch is a bust. The Touch doesn't recognize the Real or Windows Media file formats, nor does it understand Flash. All of this means that the iPod can't easily play the huge majority of online video and audio recordings.
But the iPod Touch isn't utterly clueless about streaming online goodies. It can play some QuickTime movies, like movie trailers, as long as they've been encoded (prepared) in certain formats (like H.264). It can also play MP3 and WAV audio files right off the Web. Here are a few sites to sample:
BBC News. The Beeb's podcasts stream nicely when you tap the Podcast icon and then the Download link. http://www.bbc.co.uk/radio/podcasts/directory/station/worldservice
New York Times podcasts. A whole page of different news shows that start streaming when you tap the MP3 link. www.nytimes.com/podcasts
"Meet the Press" audio stream. An MP3 edition of the venerable Sunday morning talk show can be found here: http://podcast.msnbc.com/audio/podcast/MSNBC-MTP.xml
Actually, any old MP3 file plays fine right in Safari. If you've already played through your 8, 16, or 32 gigabytes of music synced from your computer, you can always do a Web search for free mp3 music.
As for video, you have more to watch on the Web than just Touch-friendly streaming videos that you can get back at Home→YouTube. Apple, in addition to ...