You can find the performance rights to a very large majority of the shows out there with one of five companies.
Samuel French: Primarily deals with plays, but also a fairly good selection of musicals.
http://www.samuelfrench.com/store/index.phpDramatists Play Service: Like Samuel French, primarily plays, but also some musicals. For musicals they tend to pick up the smaller Off-Broadway titles (such as
Bat Boy), as opposed to the big Broadway shows.
http://www.dramatists.com/The Rodgers and Hammerstein Organization: As the name would imply, they control the performance rights for all Rodgers and Hammerstein shows, along with a good number of others. All of Andrew Lloyd Webber's shows are also controlled through them.
http://www.rnh.com/show_home.aspMusic Theatre International: Probably the largest musical catalog of the big three for musicals. They control all Sondheim shows (with the exception of
Gypsy), as well as the Disney catalog, including their Broadway titles, the
High School Musical franchise, and JR. versions of many of the animated films which have not been seen on Broadway.
http://mtishows.com/Tams-Witmark: The third in the big three for musicals. Their catalog is primarily made up of musicals from the "Golden Age."
http://www.tams-witmark.com/musical.html