As soon as we lost gravity we would start to float away from the planet because the planet is turning and our momentum is tangential to the surface of the planet. At the equator the surface of the Earth is travelling at approximately 1037 miles an hour relative to a 'fixed' point such as the Sun, so someone standing on the equator would continue in a straight line tangential to the planet at 1037mph. However, everything else not attached to the planet would behave in a similar way, including all the water, sand, rocks etc. on the planet and a lot of larger land masses too. In fact, considering the liquid magma beneath the Earth's crust it would be reasonable to assume that each tectonic plate would detatch from the core and wander off on its own trajectory, so many of us wouldn't notice a change of scenery until the sky changed due to the dispersal of the atmosphere should gravity remain lost for long enough, revealing a stunning view of our neighbouring stars as we decompress, asphyxiate and either freeze or fry depending on whether one is in view of the Sun or not. One might also notice an inability to walk due to a loss of friction with the ground; it would be possible to jump away from one's fragment of tectonic plate but not to return to it. The hot, liquid components beneath the crust of our planet would also disperse, leaving a solid core if the planet has one. On a larger scale, the Earth would fall out of orbit around the Sun and the Moon (and our smaller moons and our satellites) would fall out of orbit around the Earth and set off in their own directions. If gravity returned quickly we would come down without too much of a bump because it takes a while to get far from the surface of the planet by travelling at a tangent to it. There would undoubtedly be a fair bit of volcanic activity; San Francisco, for example, would be truely stuffed. There would already have been many accidents, including virtually every vehicle in motion when gravity was lost. Luckily our Moon (and our smaller moons and our satellites) would float off into space rather than coming crashing into Earth, but we would notice sometime afterwards, maybe a month, maybe a year, that our Sun didn't seem as big as it was before. On our moonless planet, we would travel along a trajectory slowly spiralling away from the Sun into the coldness of space, probably to the theme tune of those old Hamlet Cigar adverts rather than 2001: A Space Odyssey. Gravity: you don't know what you've got until you lose it...