I am curious about what games exist in which the player character has, or can acquire, the ability to breathe fire.

Specifically, the requirements are as follows:
* The ability needs to be fire breath. Being able to cast a fireball doesn't count.
* The ability needs to be available to the main character. In particular, the main character's mount doesn't count, even if it's a fire-breathing dragon. It also doesn't count if it's a summon (so Wizardry 4 doesn't count, for example).
* If the game has you creating your party and doesn't have an obvious main character, it needs to be possible for the first created character to have this ability.
* This ability must not be awkward to use. (This rule is intended to exclude cases like Dragon Quest 3 and 4, where it's possible for the main character to Transform into a party member who can cast a spell to turn into a dragon making the setup possible but impractical.)

Unless I missed it, you didn't specify humanoid. :)

So, Spyro the Dragon.
One of my absolute favourites.

Well, "Breath of Fire" https://en.wikipedia.org/wiki/Breath_of_Fire

I'd argue that it's impractical for regular usage because it requires a consumable of which, I'm guessing, there's only finitely many in the game.

Gargoyle's Quest

consider https://www.gog.com/en/game/divinity_dragon_commander but its an old game now so wait until you can grab it on special... the role play parts take place before and after battles with real +&- results i.e, characters die or your money\ spells\ abilites change based on which options you pick

also these older games need to be outside c program files to work and W11 will not like them

Elden Ring has a fire breath ability.
Karnov, you play a fire spitting guy.

The I of the Dragon. The fire dragon uses fire and one of the available attack types is fire breath.

The other dragons have breath attacks too, but they use acid and ice.

IIRC in might and magic 8, in your party of 4, you can find dragon PCs, who can breathe fire. They are PCs, not mounts or summons. They aren't available for a while though, since they're powerful.

IIRC, in Elona you actually can breath fire as well.

In Solasta, characters of the Dragonborn race or ancestry are able to breathe fire or other unpleasant things.

Shin Megami Tensei 3: Nocturne - There are several breath attacks that the Demi-fiend (main character) and some his demon minions can learn, fire being one of them. What makes them distinct from multi-target spells is they hit random targets, sometimes a single target more than once.

Skyrim -Fire breath along with a frost variant, are among the shouts the Dragonborn can learn.

Dragon Spirit -- This is an example I haven't played personally. A vertical-scrolling shoot-em-up with the player character being a dragon, not just riding one. Naturally, the dragon has wide variety of fire-breathing abilities. It seems had a couple of sequels as well.

There some fighting game series that have playable characters with fire-breathing abilities. They may not necessarily be the "main" characters, but some are regulars in the series' roster.

Mortal Kombat -- Whether or not he is the main character questionable, but Scorpion is one of the most iconic characters in the series. His most well-known finisher involves burning his opponent with a fiery breath, and used several times throughout the series.

Street Fighter -- Dhalsim's fire-breathing can take form several forms, from a stream of fire to a fireball.

Samurai Shodown -- Tam-Tam, Kyoshiro, and Earthquake all possess a fire breathing attack.

Tekken -- True Ogre's fire-breathing attacks are unlockable, but have a noticeable startup time. He appeared in Tekken 3 and Tekken Tag spinoffs. A guest character in Tekken 3, Gon, also has fire-breath attack.

There are several games where the player character has the ability to breathe fire, with the specific requirements you mentioned. Here are a few examples:

Spyro the Dragon series: Spyro, the titular character of the series, has the ability to breathe fire as one of his primary attacks.

Dark Souls series: The Pyromancer class in the series has the ability to cast fire spells, including the ability to breathe fire.

Breath of Fire series: The main character Ryu has the ability to breathe fire as part of his dragon abilities.

Golden Sun series: The main character Isaac has the ability to summon a dragon that can breathe fire.

Chrono Trigger: The main character Crono can acquire the ability to use a fire-based technique called "Flame Whirl" as part of his tech abilities.

Dragon's Dogma: The main character can acquire the ability to breathe fire by equipping certain items or spells.

Skyrim: The player character can acquire the ability to breathe fire by unlocking the "Fire Breath" shout.

Hopefully, this gives you a good starting point to find a game where you can breathe fire as the main character!

The wyrmic class of Tales of Maj'Eyal has a Fire Breath talent.