Coates Library, Trinity University, San Antonio, Texas, 2007. John Haskell teaches us about the sport of awkward dancing. http://www.youtube.com/watch?v=bmm4KV37-fA

Case Library, Colgate University, Hamilton, New York, 2007.
Three guys bust a move in the library.
http://www.youtube.com/watch?v=Z3lgzHGUgoM

Rich (now Rich East) High School Library, Park Forest, Illinois, 1961.
The senior class attempted to check out all the books from the library. They got about halfway done before the library staff stopped allowing checkouts.

ALA conference, Seattle, Washington, 2007.
Documentary footage and narration a la the 2005 film March of the Penguins. http://www.youtube.com/watch?v=Td922l0NoDQ&NR

Tutt Library, Colorado College, 1990s. Participants wore flip-flops and carried books instead of batons. Photo from Colorado College Special Collections (PP95-62 #94).

Similarly, Swarthmore College has the “McCabe Mile,” a race through the library. The prize is a roll of Scott toilet paper, Swarthmore benefactor Edward McCabe being a former head of the Scott Paper Company. (Thanks, Christopher Densmore!)

Medieval Help Desk, in Norwegian with English subtitles, from a Norwegian TV show written by Knut Nærum, 2001.  Not exactly a library shenanigan, but close enough. Along the same lines, a video in Spanish (without subtitles, 2010) and  a comic strip called “Progress” from Penny Arcade (2009). Thanks, Daryll Stevens and Jon Driscoll!

Golda Meir Library, University of Wisconsin, Milwaukee, 2006?
http://www.youtube.com/watch?v=Ns314ZNaJb4

Funk ACES Library, University of Illinois, 2006.
http://www.youtube.com/watch?v=cwihz7iZlx0

Addendum, April 1, 2014 (thanks, Steve Lawson!) The London Public Library in California put together a similar shenanigan in March of 2014:

Williams College Libraries, Williamstown, Massachusetts. Library-centered spoof of the A-Team. http://www.youtube.com/watch?v=YwCUtpbUWgk

A Star Wars Adventure. Whittier College Library, March 16, 2006. A light sabre battle in the stacks. http://www.youtube.com/watch?v=b2WxwzGY42Q