The three American Performing Rights Organizations (PROs) are ASCAP, BMI, and SESAC.
ASCAP is the oldest of the PROs, founded in 1914. Today, ASCAP consists of over half a million music writers, creators, and publishers. You can search ASCAP's database of music here.
BMI was founded in 1939 and is now the largest PRO. You can search BMI's database of over 8.5 million songs here.
SESAC is much smaller, with around 400,000 songs, but it has many big name artists and boasts that it pays its royalties out monthly instead of quarterly. You can search SESAC's catalog here.