using music clips ?

I want to post some video clips from my classes on my website. In the future, I may also create some DVDs and will want to post preview clips of those as well.

I notice that some people use popular (and recognizable) music in their online clips, as well as in their videos and DVDs (during the credits, for example). My impression was that this requires the artist's permission. However, I do not see people citing any of the musical sources, so I wonder if that step was completely skipped in the production of those videos, dvds, and clips. I also notice that other instructors/companies seem to work hard to create their own riffs, clips, and theme music.

So what is the final word? Can you use someone else's published music for your (1) online clips, (2) DVD/video credits, or (3) segments within a DVD/video?

~TT