NASA Select (NASA's "TV channel") coverage of shuttle missions is broadcast over the internet through two means. Macintosh and PC (Windows) users can view the video using the CU-SeeMe program from Cornell University. UNIX users can take advantage of the MBONE to view the video.
If you have a choice of platform to use, check out the MBONE as you will get better throughput (including better luck at actually connecting) and possibly less network traffic overall. This will require one machine at your organization to act as your connection. CU-SeeMe users should plan on dedicating at least one machine at their site for a local "reflector".
Participating in the MBONE requires IP multicast support. Macs are supposed to get this with Open Transport next year, and I believe Windows users will receive this functionality with Windows 4.0 (Chicago). Once this happens, the CU-SeeMe developers have said they will adapt CU-SeeMe so that it may interoperate with the MBONE.
Michael Baldizzi and Greg Madey of NASA's Lewis Research Center have set up a wonderful page on NASA Select for CU-SeeMe users.
NASA is also feeding audio. Mac users can listen to this feed using Maven. (BinHex encoded)
Xerox PARC is broadcasting the NASA Select feed (both video and audio) over the MBONE (Home Page and HTMLized FAQ).