Yes, at the GM's discretion.
Another answer says, "There is no beast feature which reduces falling damage." This is not quite correct. In fact, there's no beast whose stat block specifies that the beast reduces falling damage. The RAW allows two interpretations: If an ability isn't on a stat block, that ability doesn't exist; or, if an ability isn't on any stat block, then the rules just aren't addressing that ability (and therefore it's an edge case, and the GM can and should make something up).
Starting at 2nd level, you can use your action to magically assume the
shape of a beast that you have seen before.
While you are transformed, the following rules apply:
- Your game Statistics are replaced by the Statistics of the beast, but you retain your Alignment, personality, and Intelligence,
Wisdom, and Charisma scores...
Let's say my druid is being chased by trolls. On my turn, I say, "I jump off a cliff, but first I wildshape into a cat, causing me to suffer less harm than if I'd turned into, say, a wolf."
At this point, the GM would be credibly following the rules with EITHER of the following interpretations:
Interpretation 1: No.
The rules afford the cat shape no special consideration. Based on their stat blocks, a cat is actually worse off than a wolf; neither has a special falling ability listed, and a wolf has more hit points to absorb the fall.
Interpretation 2: Yes.
A cat is not a stat block. A cat is a four-legged, furry animal with many properties. The fact that the stat block doesn't list a common property of cats doesn't mean the cat lacks those properties.
Beasts include all varieties of ordinary animals, dinosaurs, and giant
versions of animals (Monster Manual p. 6).
In other words, the stat block for a cat is meant to model a real-world cat.
The cat jumping off a cliff is an edge case. Since the rules don't address cat falling aptitude, the question shouldn't be, "What do the rules say?" but rather, "What would the rules say if they bothered to address this issue?"
Interpretation 2 is better.
I at first wanted to offer only the second interpretation, but that's not fair. I have reasons for preferring interpretation 2 (which I'll explain), but Interpretation 1 is consistent with the rules.
The problem with the first interpretation is that it requires willful ignorance about real-world animals, and (taken to an extreme), it creates needless oddities in the fantasy world. Meanwhile, interpretation 2 is more fun, as it allows Wild Shape to be a tool for creative problem-solving.
Remember: Wild Shape specifies "a beast that you have seen before." If you're limited to turning into a cat that's bad at falling, that means that you live in a world where the typical cat is bad at falling. What other surprises await you in this strange fantasy world?
- You enter a town. It's an ordinary medieval town, and yet, something seems off. Yes, that's right, none of the cats are light on their feet. It's the spooky fantasy element that no one asked for.
- The party enters the tavern. There, in the corner, is a dog pooping in a litter box. That's right: because its stat block doesn't say how pet dogs are maintained, we have to assume that they're basically the same as cats. Again, spooky fantasy element that no one asked for.
- The party encounters a giant octopus. The bard walks over and starts petting its soft, lustrous fur. Wait, what? Sorry; stat block doesn't say whether giant octopuses have fur, so they're probably the same as cats and dogs in that respect.
Real-world cats and falling
It's worth noting: real-world beasts are NEVER magically-good at falling. Cats are exceptionally good at falling, and yet they sometimes are injured or killed by falls. If a GM wanted to make the "Cat jumps off a cliff" outcome realistic, or at least exciting, he might decide a skill check and/or saving throw was in order. Maybe the druid-cat gets banged up to the point of reverting to a humanoid. Maybe that happens when the cat hits the ground, or maybe it happens when he collides with a tree branch 20 ft off the ground.
The bottom line for Interpretation 2 is: The GM needs to make a judgment call based on BOTH things like whether there are trees or other hazards AND how good he thinks a chosen beast-form might be at negotiating those hazards.
Like I've said, the above is a detail that requires GM interpretation. If your GM wants to argue that a beast is no more than its stat block, fine. Take the ruling and move on.
There are a couple things, though, that the rules definitely DO say about Wild Shape in relation to your question:
Is there any unambiguous way for Wild Shape to prevent fall damage?
Yes; a bird-shaped druid can descend using the movement rules (without it counting as a fall).
Can a falling druid activate Wild Shape?
No. Wild Shape requires an action (or a bonus action if a Moon Druid) As this question explains, you don't get your turn to take an action before going splat, unless the height is greater than 500 ft. and you're using an optional rule.