The sites listed below are commercial sites. They provide a nice selection of free plays and monologues as well as many products for sale. Be aware that you may encounter many ads and pop-ups when using these sites.
A variety of monologues: comic, dramatic and classical. Search for monologues for men or women or for children and seniors. Also searchable by playwright.
Find a Monologue section provides over 300 monologues sorted by genre and age group. On home page scroll to StageAgent Resources (mid-screen). Click on Find a Monologue.
"Offers over 46,000 free ebooks."--Project Gutenberg Included in the mix are plays by Anton Chekhov, Bernard Shaw, Joseph Conrad and more. Use the search box on the right. Enter "one-act plays" or try searching with the term monologues.