The movie was Any Given Sunday, and they were the Miami Sharks I believe. Hence they did the Shark thing. LL Cool J was the RB. Jamie Foxx was the hot shot Michael Vick-style QB, Steamin Willie Beamen. Lawrence Taylor was in it I believe as well.
And yes they did the shark motion thing.
Also, I think it was actually Powe that started it. He was the only one I saw doing it early in the year, and apparently it caught on as the season went on. I like it for the reasons OP4 stated. It gives the defense an identity and a swagger.
Much like I think MSU should try to steal the Christopher Walken "Need More Cowbell" bit to play on the Jumbotron, I think we should steal the old SNL "Landshark" bit to play on ours. I'm sure that copyrights are an issue that would keep either from happening, but both would be a good idea.
Edited to add: Check at about the 40 second mark, from Any Given Sunday
<embed src="http://www.youtube.com/v/7lWJRSL-JBQ&hl=en&fs=1" type="application/x-shockwave-flash" allowScriptAccess="never" width="425" height="344" ></embed>
And I definitely remember seeing it during other parts of the movie during the actual games, as one of their celebrations.