As suggested by one of the answers to this question on holding breath, there can be situations where damage may be able to be avoided by holding your breath.
A creature can hold its breath for a number of minutes equal to 1 + its Constitution modifier (minimum of 30 seconds).
When a creature runs out of breath or is choking, it can survive for a number of rounds equal to its Constitution modifier (minimum of 1 round). At the start of its next turn, it drops to 0 hit points and is dying, and it can't regain hit points or be stabilized until it can breathe again.
Consider cloudkill:
When a creature enters the spell's area for the first time on a turn or starts its turn there, that creature must make a Constitution saving throw. The creature takes 5d8 poison damage on a failed save, or half as much damage on a successful one. Creatures are affected even if they hold their breath or don't need to breathe.
And stinking cloud:
Each creature that is completely within the cloud at the start of its turn must make a Constitution saving throw against poison. On a failed save, the creature spends its action that turn retching and reeling. Creatures that don't need to breathe or are immune to poison automatically succeed on this saving throw.
The wording is a little confusing, does holding your breath count as not needing to breathe for purposes of potentially avoiding damage? What are the situations where holding your breath will allow you to avoid taking damage for the duration of your ability to hold your breath?
Best Answer
If a creature doesn't need to breathe that means it (basically) never needs to breathe; I found no features where holding your breath is helpful, only features where not needing to breathe is helpful
The cloudkill spell shows us that "not needing to breathe" and "holding your breath" are indeed different things, otherwise there would be no reason to list both.
Not needing to breathe is not defined by the rules so we would use the standard English meaning of "not needing to breathe" which is that something never needs to breathe.
If I say that a fish needs water to survive it doesn't mean that the fish needs water right now it means that they always need water.
Similarly, if I say that a human doesn't need cobalt to breathe it doesn't mean that they don't need cobalt right now it means that they never need cobalt to breathe. (Extreme situations where somehow cobalt is required for breathing could exist, but this just shows that "never needs cobalt" isn't really a phrase that works; it really means "in all likely scenarios, won't need cobalt")
I found only two mentions of the rules where breathing has negative effects:
High Altitude (DMG page 110):
Suffocating:
Holding your breath is arguably "helpful" here but it's also effectively not a choice. You would be holding your breath unless you specifically chose not to. Additionally you can only suffocate if you actually need to breathe in the first place. Not needing to breathe would thus protect you from anything which causes you to suffocate, such as quicksand (DMG page 110).
Unfortunately, neither of these are removed by holding your breath, as you would still be a creature that needs to breathe.
Even Inhaled Poisons still affect a creature holding their breath as it says (DMG page 257):
There is also an item from Volo's Guide to Monsters; the Survival Mantle (page 81) which states:
This seems to list the things which relate to breathing; however, I've now checked the listed spells, inhaled poisons, and all breath weapons that dragons get. None of these have any text saying that holding your breath will do anything to counter them.
Regarding the clarifying text at the end of each spell:
A spell affects anything that isn't explicitly stated as not being affected. The cloudkill spell likely calls out that it does effect creatures that can't breathe simply because it would be a common point of confusion, and a disconnect from our real-world logic, if a gas was somehow affecting creatures which can't even breathe in said gas.