After several years of perplexing the Internet, this quote has been found a few years ago. Like many quotes from pre-Internet times, it got a little mangled in the remembering. Turns out it's from an old police drama called Burke's Law.
The Episode
Burke's Law was a police drama that ran from 1963–1965. The episode Who Killed 711 was the 12th episode of season 2. IMDb summarizes the plot: "When a businessman, Buddy Jack Cook, with a very shady reputation is found slain in a hotel elevator, Harold Harold, his accountant, is the prime suspect." The episode name refers to Cook's room number at the hotel, 711. After arresting Harold but remaining unconvinced that Harold did it, Captain Burke goes undercover at the hotel to find the real murderer.
The Quote
About 9 minutes into the episode, Captain Burke interrogates Harold Harold (Burgess Meredith), finding him working on complicated contraption in his hotel room, which, among other things, spins a propellor and rings a bell. The nebbish, stuttering man explains the gadget to the police, and herein we find the mangled quote:
Can you turn this thing off?
Oh, certainly. Certainly. I always take this with me when I travel. At home I have a much bigger one.
What is it?
Well it's my therapy. I'm still perfecting it.
What does it do?
DO!?
What's it for?
Well, nothing, nothing. I mean, that's the beauty of it! Every machine in the world does something but not mine. This is my rebellion against efficiency! I also work puzzles.
The exchange is meant to establish Harold Harold's character, a small, nervous man more comfortable with machines (and numbers) than people. It's absurd to think he might have committed the murder, and Burke doesn't believe it any more than the audience does.
Beam Me Up, Scotty
Mangled quotes are nothing new. Kirk never quite said "Beam me up, Scotty." Rick Blaine didn't exactly say "Play it again, Sam." And Darth Vader only almost said "Luke, I am your father."
For the most part, people are working off of their memories for these quotes, and human memory is infamously malleable. Over time, I believe the best versions of the quotes are the ones that get passed on and into popular culture. If you look at the original quote, exactly as delivered by the actor, in any of these cases, you'll find they don't stand alone very well. They depend on the context of the scene and make for better dialogue than a one-liner. The mangled quote becomes self-contained, still recognizable but rearranged or including enough bits from the rest of the dialogue to stand alone.