Fall damage

Fall damage refers to the damage a player character sustains upon falling a large distance. It is one of the basic game mechanics. Fall damage occurs only if the "fall distance" exceeds a fixed threshold, beyond which the damage amount varies linearly with the distance traveled past said threshold. If the damage amount is greater than or equal to the player's current health, he or she dies upon impact.

Perhaps surprisingly, the player's vertical speed upon impact has no bearing on fall damage. Fall damage works the same way for all solid surfaces, but does not occur when submerged in water or lava. It is mitigated by the player's Defense.

Formula
In the basic case—falling through air directly onto a solid surface, without the use of special accessories or potions—fall damage is affected by exactly two variables: fall distance and Defense. No damage is sustained if the fall distance is less than or equal to 25 blocks (50 feet). Beyond this distance, 10 additional damage is sustained for each block traveled (or 5 damage for every foot). Thus, assuming a distance greater than 25 blocks (and no Defense), the formula for calculating fall damage is damage = 10(h - 25) where h is the total fall distance (in blocks). To factor in the player's Defense rating, simply apply it in the normal way: damage = MAX( 1, 10(h - 25) - ROUND_UP(d/2) ) where d is the Defense rating. Note that the MAX function clamps the result to a minimum value of 1, because an injury always causes at least 1 damage, regardless of Defense.

Negation/strategies
There are four major ways of negating fall damage and three minor.

Stopping the fall
The first and most obvious is to "break" the fall before hitting the ground. Using items such as Cloud in a Bottle, Rocket Boots, Grappling Hook, Ivy Whip, or Dual Hook will cause the fall distance counter to reset upon use, negating the damage. You can also make a pool at the bottom of your descent, useful for hellavators, or put Cobweb. Cobwebs slow you down, so if you put it right before you land, you will not suffer any damage.

Preparing the terrain
Another alternative is to prepare the terrain in such a way as to not take fall damage at all: Placing wooden platforms inside shafts so that the fall distance never exceeds 25 blocks. Other alternatives include cushioning the ground: Cobwebs or a sufficient level of Water will stop the player's fall, without damage. As of version 1.0.6, Cobwebs will break off after pushing them. This makes water the more desirable choice as the player would take the cobwebs with them.

Accessories
The Lucky Horseshoe is an accessory that negates fall damage. It can be found in Floating Island chests. They can be very handy when exploring chasms. It can also be combined with an Obsidian Skull to make the Obsidian Horseshoe, which has the benefits of both the Skull and the Horseshoe while taking only one accessory slot.

Once the player has found a Grappling Hook and/or a Cloud in a Bottle, the Lucky Horseshoe loses some of its usefulness, and can potentially be swapped out, although having one equipped is always a good safeguard.

The Angel Wings and Demon Wings also offer complete fall damage immunity on top of their flight, slowfall, and stacking with Spectre Boots, effectively rendering the Lucky Horseshoe obsolete once obtained.

Featherfall Potion
The Featherfall Potion makes players fall more slowly and negates fall damage, even when its slowing effect is temporarily canceled out by the player holding the down key.

Cobweb parachute
By falling next to a wall and placing a Cobweb under you before you land, you can negate all of the fall distance above the cobweb you placed. This is almost never used because cobwebs can only be placed over a background wall piece or by a block, but cobwebs are easier to come by than other items so that makes them good to start with.

Bucket parachute
By using a Bucket to pick up water and then drop it below you during a fall, you will find that you are falling almost as slow as the water, thus not "actually" falling. This can be good for spelunking into large caves and the corrupted area due to many of these places often having water on the bottom and you can often salvage the water you drop. (You could do this with lava too but if you don't have the Obsidian Skin buff active during the whole thing you would take lava damage and would probably die.)

Sand ladder
If there is an area with a large drop or may be hazardous (such as a lava pool), gather a lot of Sand (the number of blocks you want to avoid falling or more). When you reach an area you want to go down, drop sand down there until it has stacked up to a desirable level, jump onto the pile of sand and then mine the sand block you're standing on.

Maximum fall damage
Although there is no maximum cap on fall damage, there is a limit to how big your map can be.

On a large world you can take up to 23270 damage if falling from the top of the map to the bottom. This would mean falling down 2352 blocks (after 25 blocks). So from the bottom of the map to the top of the map (that a player can have access to) is 2352 blocks + 25 + 2 (because you land on your feet, you have to account for your body and head too) which makes a large world 2379 blocks in height, or 4758 feet (again, that a player has access to. There is space outside of the boundaries for monsters to spawn).