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Sometimes gravity doesn't work. Or doesn't work immediately. Or evenly. Or fairly. This takes the following forms:
Gravitational Cognizance: A character will not fall until they realize they should be falling. For example, running unknowingly off the edge of a cliff — or walking on the underside of a diving board. Especially dense or focused characters may need to have another character point out their vulnerability.
An occasional variant has a character, upon realizing their situation, desperately start scrambling back where they came from, often managing to reach the original ledge before gravity can notice.
In an episode of Tiny Toon Adventures, the characters invoked this trope to pass over a gorge by stepping on thin air without looking down. Makes you wonder after a while why anyone looks down at all.
In The Hitchhiker's Guide to the Galaxy flying is the art of deliberately (ab)using this trope. Specifically, throwing yourself at the ground and missing, and then making sure not to think about the fact that flying is impossible, or else gravity will notice you.
In Dungeons & Dragons, some Elemental Planes have "subjective directional gravity," which essentially means that "down" is whichever direction you think it is. As in the above example, some mental gymnastics make it a very effective method of getting around within those Planes.
On more than one occasion in WB shorts, a character who was falling to earth gently via parachute was handed an anvil... by another character who was falling at the exact same rate... and immediately went into a terminal velocity plunge.
Characters will fall faster than a heavy object — ensuring that the object lands on them. Everything falls faster than an anvil.
Sometimes gravity will even shift around the relative positions of objects. For example, a character and an anvil are falling side-by-side, when suddenly the anvil starts falling a bit slower and moves laterally so it is now directly above the character's head. Wile E. Coyote is intimately familiar with this variant.
Gravity can be suspended for just enough time to give one last comment to your opponent. For example, in the Looney Tunes short "High Diving Hare", Yosemite Sam, after being tricked into falling off a diving board by Bugs (for the fourth time), rose back up for a moment to say, "Ah hateyew," before plunging again.
Gravity can also be suspended while a badly spooked character bobs up and down in mid-air while screaming, for example Tom of Tom and Jerry.
Out On A Limb: Gravity is less powerful than other physical forces, including friction, tension, torsion and all the rest. Static electricity appears to be the most powerful physical force. This allows objects to be stacked on top of each other across an unlimited space or height, maintaining stability even if the branch or beam they are standing on is sawed in half, so long as the pieces are touching. This also allows characters to balance an unlimited number of objects in their hands.
Counterintuitive Gravity: Items which should fall don't, when items that shouldn't, do.
The traditional case is a character chased up a tree and out onto a limb, as above. It is reasonable for them to trust their weight to a branch while the chaser is cutting through it, because sawing the branch off will make the tree fall. The section being removed (and the character on it) remains suspended in mid-air while the rest of the item (plus whatever object or structure had been supporting it) falls, presumably forever.note This could be because It's Turtles All The Way Down. Diving boards and bridges are also prone to this effect.
This is explained by Bugs Bunny in the aforementioned "High Diving Hare" short. At the end of the episode, Yosemite Sam tries to saw off the end of a diving board, with Bugs on it. However, the diving board ladder, and part where Sam is, fall down, leaving Bugs and the end floating. Bugs remarks "I know this defies the law of gravity but eh, you see, I never studied law", suggesting ignorance of the law of gravity, equals it not noticing you, thereby allowing the situation.
The Road Runner and Coyote lampshade it in a cartoon where they use signs to communicate the same thing.