What would happen if the Earth lost gravity?
First of all, if the earth suddenly lost gravity, we'd not be attached to it any longer and so we'd rise in a straight line, while the earth kept spinning under us. But we'd have the strange feeling that the earth was dropping away from us, not that we were rising.
When astronauts do not have gravity pulling them down, they sometimes feel sick initially, until they get used to it. But still, their arms and legs can feel disconnected, and they can grow up to an inch, as their bones are released from the pull of gravity. (They go back to normal when they get back into gravity situations). Their muscles weaken and they have to exercise to be able to move properly. Sometimes they can't see properly. That's why they have all that gear, to neutralize some of these effects.
Without gravity, the earth's gasses would float off, too, so if you were tied to the earth somehow, you'd be okay in a building for a little while, but then you'd need an oxygen tank to breath. But bad news: without the air, or atmosphere, the earth would get hot very quickly. The sun's heat would cause the lakes and oceans to overheat to the point of boiling, and then water would disappear, too -- first in large blogs, and then through evaporation.
Then, buildings would start to fall apart, and indeed, the entire earth would crumble and float away into space.
So the simple answer to the question is this: No gravity, no earth.