An implication of that idea is that antimatter should curve up against gravity. Until sometime in the 80s, no one could tell for sure about this, since subatomic particles are very light and don't bend much under most conditions. Finally, the work got done and the answer recorded: antiparticles have the same mass, the same gravity as normal particles.
You don't see many stories featuring antigravity anymore.
HG Wells took a ship to the moon by coating it with an anti-gravity paint of some kind, so the ship didn't weigh anything (probably an early form of WD-40). That was written about 100 years ago, typical of the period. But you're right, SF just doesn't use anti-gravity these days.
With good physical reason. Without gravity, you no longer have strong, overwhelming force acting on you. That is, you will remain in place (assume no residual velocities).
However, the earth will continue to rotate, continue to move around the Sun. The solar system will continue to move within the galaxy. The galaxy will continue to move in the cluster of galaxies, the cluster of galaxies... You get the idea. I think I read somewhere that we have something like 40-80 known forces acting on us.
Now, if you turn on that anti-gravity puppy in your basement, will a wall, the floor, or the ceiling smash into you?