I'm fairly certain by the way this is worded that you're looking more for a fantasy-like scenario where people can float around on giant islands, but I think I'll give a more realistic response.
The Earth, no longer bound to orbit the Sun, would be flung off into space. Also, it would probably explode from the internal pressure no longer being opposed by gravity. Most if not all life on Earth would die within the first few seconds. I'm not sure exactly how much influence gravity has over a single human body, but since it is likely minimal, it's possible some people would survive for hours, or even days in small bunkers. Eventually, though, they'd run out of food, air, or heat. Which they'd run out of first would likely depend on what sort of shelter was protecting them.
I'll love an entire day of that. Just one day though. But what if, since it is the universe flipping the switch on gravity and so made it that no one dies of hunger or heat or air, just what if? Would people, with their ever creative minds, the best scientists in the world for instance, still be able to figure out something or some routine to sustain life in that kind of mess? I'm just really curious.