According to Nintendo, Mario is no longer a plumber. As spotted by Kotaku, the character's profile on Nintendo's official Japanese-language website states that Mario used to be a plumber:

All around sporty, whether it’s tennis or baseball, soccer or car racing, he [Mario] does everything cool. As a matter of fact, he also seems to have worked as a plumber a long time ago...

The Nintendo website also features profiles on other prominent characters in the Super Mario Bros. game series, including Luigi, Princess Peach, Toad, Bowser, Yoshi, Daisy, Wario, Waluigi, Rosetta, Bowser Jr., Boo, Donkey Kong and Diddy Kong.

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When Mario was introduced in the 1981 Donkey Kong arcade game, the character was known only as Jumpman. Video game designer Shigeru Miyamoto said that the character was originally a carpenter, since the game took place on a construction site. Mario Bros. introduced Mario's brother Luigi in 1983, and the game took place underground. It introduced the concept of warp pipes, so Nintendo played up the theme and made the characters plumbers instead. Mario was explicitly depicted as a plumber in The Super Mario Bros. Super Show! from 1989 and the Super Mario Bros. live-action film from 1993.

In his history, Mario has also been a construction worker, referee, pilot, doctor, racecar driver, chef, archaeologist, toy maker, street dancer, theme park owner and olympic athlete. If he's no longer a plumber, it's likely by choice, and he should be fine out there on the open market.