The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at the Trope Launch Pad.
I see this listed as Sampling in the page for Machinae Supremacy. For example, they sampled Hugo Weaving saying "Welcome to Rivendell, Mr. Anderson," and put it in one of their musical compositions.
There is also Spoken Word in Music.
Edited by KDCool. I was seeing it on Manic Street Preachers, they use quite a few movie quotes at the beginning or end of various tracks on a few of their albums. Just wanted to make sure there wasn't something more specific.

A spoken quote from a movie, TV or radio series added to a musical track, as in the page quote for Techno. Can be repeated or not. Does this just fall under Sampling? Just checking.