From the Super Mario Wiki
Inspector Gadget, also known simply as Inspector or Gadget, is a bumbling detective cyborg who has starred in many animated TV series, specials, and two live-action films. He is well-known for the fact that his mechanical body contains a huge variety of gadgets, most of which are activated by him saying "Go-Go-Gadget-(name of gadget)". Inspector Gadget appeared as a guest star on The Super Mario Bros. Super Show! on two occasions.
DIC Entertainment produced the 1983 animated Inspector Gadget series, and has used the character as the company mascot. As such, an animated version of Inspector Gadget is featured in the menu of the The Super Mario Bros. Super Show: Mario's Greatest Movie Moments DVD, where he explains how to use the menu's various options.
Inspector Gadget first appears in "Defective Gadgetry", where he arrived at Mario Brothers Plumbing in need of repairs. It was the character's first live-action appearance, predating the film by ten years. As he greets Mario, the two of them shake hands, only for Gadget to accidentally extend his gadget hammer in place of his hand. Mario pulls off the hammer and tells Inspector Gadget to return in an hour. Inspector Gadget replies that he has to stay while Mario and Luigi repair his gadgets, as he is awaiting an important phone call from the Chief. Gadget then answers the call on his top-secret gadget phone, and tells the Chief that he is on his way as soon as the Mario Bros. fix him up. As Gadget hangs up, the antenna on his phone breaks, prompting him to complain about falling to pieces.
Inspector Gadget waits patiently while Mario and Luigi repair his body. Despite what they claimed, Inspector Gadget's body is now in worse shape than when he had arrived, as it is in pieces all over the assembly table. Barely able to talk, Inspector Gadget asks Mario and Luigi how long the two of them had been working for Doctor Claw, his longtime arch-nemesis. Fortunately, Mario and Luigi are able to rebuild Inspector Gadget's body using some spare parts that Luigi picked up. Treating Inspector Gadget as if he was a car, Luigi treats him to a bench check, reporting that his RPM is up by 3000, his oil is clean, and that he has to come back for a left foot alignment at around 3000 miles. Mario then presents Gadget with a thirty-day parts-and-labor warranty, and warns him not to run over any nails.
As he prepares to write out a check, Inspector Gadget asks Luigi where he got his spare parts; Luigi replies that they are from a nearby novelty store. Inspector Gadget realizes what this means, and when he stands up, his hands droop down from his arms on springs. Gadget sarcastically thanks the Mario Bros. for their "work", and vows to leave before they can try and help him again. As Gadget steps outside, he accidentally activates his rocket shoes, which were wrongly hooked up by Mario and Luigi, and goes crashing outside Mario Brothers Plumbing.
Inspector Gadget later appears in "Treasure of the Sierra Brooklyn". When Mario and Luigi find a treasure map, they call Inspector Gadget over to get help.