The Illinois High School Association began a basketball tournament in 1908.  By the 1930’s, it was referring to it as March Madness.  By the 70’s, it had become an official name for the tournament.  It’s unclear (to me) when the NCAA (and Brent Musberger) began referring to its tournament as March Madness but it did begin licensing the mark around 1973.  IHSA sued but failed to enjoin the NCAA use.  IHSA v. GTE VantF.3d 244 (7th Cir/99/1996).  Some settlement ensued and the marks appear to be pooled in an entity controlled by both the NCAA and the IHSA, and both parties use the mark (the IHSA differentiates its usage somewhat by using the term “AMERICA’S ORIGINAL MARCH MADNESS”).  IHSA MARCH MADNESS merchandise is available here and NCAA March Madness merchandise is here.

Neither side claims exclusive rights to the concept of the office pool.

UPDATE:  Patrick Jones at the must-read points out March Madness Assn v. Netfire, 162 F. Supp.2d 560 (ND Tex 2001) for more on the history of the ownership of the MARCH MADNESS mark.