Lime Cultivist
Dragon Games
Golden Treasure: the Great Green

Was there ever any doubt this would be first game on the list? Golden Treasure is not only my favorite dragon game out there, but likely my favorite game ever made. The gameplay is a mixture of visual novel, choose-your-own-adventure, and RPG, where you spend each day of your life as a dragon exploring, hunting, battling in simple rock-paper-scissors style combat, and making decisions that can save or ruin your run.
Golden Treasure's strongest aspect, without a doubt to me, is its writing. The game does an incredible job at putting you inside the mind of a dragon, and the story and prose throughout Golden Treasure are downright magical, focusing on topics such as life and death, nature, compassion, self identity, and so much more. Golden Treasure still to this day has some of the most emotionally moving and satisfying moments I've experienced in a game, and I can't thank it enough for that.
Of course this game has some problems as well, such as unskippable text, which can make replaying Golden Treasure tedious. Combat is unbalanced, with some abilities like power strike being very strong, while other abilities like the true song of dominion are useless. Grinding for animal masteries is tedious, too. And the hunting minigame is janky.
The art and music of Golden Treasure are fantastic. Almost every part of this game feels polished and well thought-out, and it's clear that Golden Treasure was a labor of love more than anything else. The devs of Golden Treasure, Dreaming Door Studios, are currently working on a sequel to the game called Hierophant, so expect to see that one on this list too when it comes out!
An artistic masterpiece.
The first playthrough of Golden Treasure takes around 8-12 hours, and at least double that if you want to see every ending. Your first run will be the hardest, but it does get easier after that.
The Mystery of Caketropolis

Caketropolis is an RPG-maker mystery game where you play as a young gray dragon named Rimentus. While this game has its goofy moments (how can you not with a name like Caketropolis?), it was also created with a great message at its core. The story focuses primarily on the tensions between humanity and dragonkind, and Caketropolis has several surprising revelations that keep it interesting as you explore the small game world and unravel its mysteries.
The visuals of Caketropolis are very standard RPG-maker fare, but the music is great. General gameplay consists of simple puzzles and exploration. These do their job, but it's really the story and characters that take center focus here. One of Caketropolis's most unique features is Rimentus's ability to examine, smell, lick, or boop any object or person he finds. Try these out at various points, and you can get some pretty funny results!
A playthrough of Caketropolis takes about 3-4 hours.
(Fun fact: I use a Fleur mousepad with my current PC setup)
Scales of Stardust

A basic but fun (and free) 2D-platformer. This one has some great movement options inspired by games like Ori, and I find it to be highly replayable. Simple but nice pixel art, stock music that manages to fit the level themes well, and lots of speedrun potential. Our blue dragon protagonist is adorable, too.
Playtime is a brief 15-20 minutes, and even less on replays.
DRAGON: A Game About a Dragon

This is without a doubt the stupidest dragon game I've played, and I mean that in a good way. Dragon Game (as I'll call it from now on) is a level-based 2D platformer. Jumping and attacking are both slow and awkward, projectiles can hit you from offscreen, and some platforming sections contain blind jumps. Overall you'll run into plenty of jank while playing it.
Where Dragon Game succeeds, however, is in its humor. As you can see from the screenshot above, all the artwork was drawn with crayons, and the whole game is filled with funny dialogue and visual gags.
I wouldn't recommend this one if you're looking for a game with fast and fluid combat or platforming. But if you want to play as a dragon who speaks Haitian Creole and smokes weed with wizards while on a quest to rescue his human girlfriend, then I recommend Dragon Game for some dumb, good fun.
Playtime is about 2-3 hours.
The Dragon's Last Flight

Despite being in alpha as of now, Dragon's Last Flight is still good enough to recommend. This one is a pure visual novel where you play as an elderly man named Marius who encounters one of the last remaining dragons in the world.
Dragon's Last Flight is the 2nd best written dragon game I've played after Golden Treasure. It touches on topics of aging and death in a thoughtful and mature way, and from such a rare perspective in visual novels as well. The artwork is nice, and I quickly fell in love with the 2 main characters and the relationship they build as the story goes on. While this game does have a few issues to iron out before release, I can already tell that the ending is going to be a giant punch in the gut, and I wouldn't have it any other way.
It's hard to give a time estimate on this one, but the current alpha build is at least a few hours long.
Perihelion

Perihelion is another visual novel in alpha, similar to Dragon's Last Flight. Only a single route is available right now, but it already has some lovable characters and nice art. The biggest criticism I have is that the dragons don't feel much like dragons, and I hope this aspect can be improved as the game is updated.
Lark is a wonderful character, and her story is both personal and heartbreaking, touching on the difficulties one can face juggling family, illness, and various other responsibilities all at the same time. I love Lark's feathered design and natural colors, too.
Honorable Mentions:
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Angels With Scaly Wings - I have great memories of this game from 2019, but now, years later, my thoughts on it have become more mixed. The characters are generally likable, but the story is a mess of plot holes, time travel shenanigans, and poor worldbuilding. Still worth a try for fans of dragon visual novels.
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Dragon's Wake - Not bad, but a rather basic and clunky platformer in the same vein as DRAGON: A Game About a Dragon.