The best way to search for monologues is to use a subject heading keyword search and the word "monologues." This will show you collections of monologues held by the Marx Library.
2009 : the best men’s stage monologues and scenes
Audition monologues -- power pieces for women : a collection of dramatic and comedic one-minute monologues designed for ages 18 to 80
Classical monologues for men
Once more unto the speech, dear friends : monologues from Shakespeare’s first folio with modern text versions for comparison
One on one: the best women’s monologues for the 21st century
Shakespeare for one : men : the complete monologues and audition pieces
Shakespeare for one : women : the complete monologues and audition pieces