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From purely physics point of view, there would be no earth left, as no gravity means no mass. But, leaving this point aside, let's see what else will happen.
Oceans, rivers and lakes will float away. Entire atmosphere will vanish, only vacuum will be left. Everything on the surface of the earth including humans, cars, rocks, etc., will become weightless and float away into space. Things which are rooted into earth like trees, bridges and buildings will remain, but not for long.
On a funnier note, anybody will be able to lift heavy weights, football will become a one kick game and there will be no need of stairs or elevators. Finally, earth will also start breaking into chunks as it is held together by gravity.