It's from a Three Stooges movie, "Gents Without Cents" made in 1944. Curly says "Niagra Falls" and Moe (who was under some sort of post-hypnotic suggestion? I don't remember) turns on him and launches into the speech. (I dunno. Seemed funny when I was a kid.) See www.imdb.com for good sources of movie quotes, trivia, etc.
This was also from an Abbott and Costello movie entitled "Lost in A Harem".
Many of Bud and Lou's best-known routines were vaudeville and/or burlesque standards. The "Niagara Falls" bit ("Slowly I turned, step by step, inch by inch...I took my revenge.") was performed by many vaudeville teams before becoming identified with Abbott & Costello.


http://www.youtube.com/watch

The original author of this timeless chestnut of American Burlesque was the legendary Joey Faye. Joey started in the Borcht Belt in the Catskills and made his way to Minsky's Old Republic in the 1930's after working in radio, writing for and directing Kate Smith and Bert Lahr. Joey was a prolific writer of the great sketches,amassing 8000 of them, including "Floogle Street" which was later performed by Abbott and Costello. (Susquehanna Hat Co.)
He later went on to the legitimate stage and films. His career spanned 70 years with seamless transition in all phases.
He won an award for his performance in Samuel Beckett's "Waiting For Godot" opposite Jack Albertson playing Estragon.
He would be 100 years old this year.

It is an old Vaudeville sketch that predates moving pictures, but was used by both the Three Stooges and Abbott and Costello in movies.

The actual author of the sketch is lost to history.

I don't know the answer but I remember hearing it on the "Three Stooges Show" which played every weekday after school. Whatever happened on the show was acted out the next day on the playground at Osage Elementary School in Los Angeles and we couldn't get enough of it.
My yoga teacher, nowadays, while explaining the benefits of certain postures, will say in almost every class when we are doing something, "Inch by inch, the tendons and muscles start to repair themselves so don't be discouraged if you can't do it now. Keep trying and sooner or later, your body will heal." Well, every time he says, Inch by inch", I go back for a few minutes to the playground acting out the latest Stooges' routine seen the day before. Yoga is good and so were the Stooges.