Answer:
It Depends... If the monologue is part of a play you can buy many famous plays in book form at bookstores and through online book retailers. If the monologue is part of a movie, check screenplay websites like SimplyScripts (http://www.simplyscripts.com/), which offer free online screenplays or Drew's Script-O-rama (http://www.script-o-rama.com/).
Some theater monologues are royalty-free, search incompetech theater scripts (http://incompetech.com/theaterscripts) or euquefiz (http://euquefiz.com) and some of them are in public domain or search Free eBooks by Project Gutenberg(http://www.gutenberg.org/wiki/Main_Page)