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troperville

The character "Ryuu" means "dragon" in Japanese, and as such, its use as a name or part of a name in Japanese media tends to have meaning. But even more interestingly, throughout the years, a certain archetype has formed around the name. Characters named Ryuu or who have the syllable Ryuu in their name have many of the following character traits in common:

Male.
Usually the protagonist of their work, or at least an important secondary character.
They're pretty much universally good guys.
They tend to be young, between mid-teens and late 20s. If they are older than that, they usually didn't start that way in the series, instead having grown older as the series went along. If older than that, they tend to be mentors or father figures.
They tend to be good fighters, if not the best in their series, but they might not start that way, growing into it as the series moves along.
They have outgoing personalities, if not downright Hot Blooded.
They HATE injustice with a passion. Even if they're not actively heroes, seeing some kind of injustice committed before them is a surefire Berserk Button. A an extension of this attitude is that they usually have Papa Wolf and Wife-Basher Basher tendencies: it is not a good idea to hurt a kid or a woman in front of a character named Ryuu.
They usually suffer in full of The Dulcinea Effect. If a woman is in trouble in front of a character named Ryuu, he WILL jump in to protect her, no matter who she is. If the woman's a bad girl, this action might even make her change her ways.
They tend to have a rivalry with another character. The rival, to fit the pattern, tends to be associated with the tiger.

Do keep in mind that this is not universal (for example, Ryuu Soma of Argento Soma is quite a dark and nihilistic character), but it is common enough that it's become a pretty well recognized phenomenon. Also, the character Ryuu can be replaced by the word Tatsu(the character for Dragon in the Eastern Zodiac), while still having the characteristics of this type of character. The character Ryou is also frequently used to similar effect.

The correct pronunciation is difficult for anyone who isn't a native Japanese speaker — the "r" is actually a sound halfway between r and l, with a "pop" at the end. Pronouncing it "Dyoo" is a close approximation — it would sound a little off to a native speaker, but not as much as "Ree-oo". "Rye-oo" should only be used if you are already bread.

Examples:

Ryuu from Street Fighter. His rival is Sagat, who's associated with the tiger.
- Although the kanji used to spell Ryu's name in promotional materials for the original Street Fighter stood for "prosperity", not "dragon".
Ryuu, Raoh's son from Fist of the North Star.
Ryuuhaku Todou of Art Of Fighting / The King Of Fighters.
- Technically, the main protagonist in that series is Ryo, who is associated with the tiger. In an odd subversion, his lifelong pal and training partner, Robert Garcia is the one associated with the dragon, but he's the 'Ken' of the series...
  - Also, Ryuuhaku Todoh has never been a playable character in The King Of Fighters, though he was playable in Capcom vs. SNK 2: Mark Of The Millennium and his daughter has been a playable character in KOF from time to time...
Kazuma Kiryuu from Ryu ga Gotoku. In a subversion, though, his rival in the second game is Ryuuji Goda, another dragon-themed character(although he's more a Noble Demon than a full-blown bad guy, and he still exhibits many traits associated with his name).
Ryuu from Breath of Fire. Many of his companions are tiger-themed to contrast with him, and, well, he's a literal dragon.
The -Ryuu robots from GaoGaiGar.
Ryou Saeba of City Hunter. His lechery makes him kind of a weird fit, but he definitely fulfills this trope.
Ryouma Nagare of Getter Robo.
Ryuudo from Grandia II.
Ryuu Hayabusa from Ninja Gaiden.
Dragon Shiryuu from Saint Seiya, except maybe for the personality part. Also counts for his son Ryuuhou from Saint Seiya Omega.
- Yes, Shiryuu is much calmer and collected than his fellow Bronze Saints. No, it does not stop him from being hot-blooded as all hell.
Strider Hiryu.
Ryuuichi Naruhodo, AKA Phoenix Wright. In the third game, he actually gets impersonated and threatened by a gangster named Furio Tigre, aka The Tiger (Toranosuke Shibakuzo, aka Zenitora), who's obviously associated with tigers.
- The only element of this trope that doesn't really fit Phoenix is "good at fighting". However, he is a playable character in Ultimate Marvel vs. Capcom 3, even though he can't fight worth beans in his own series.
  - He's not that great in UMVC3 either... But then again, what did you expect putting a lawyer in the fighting arena with superheroes, supervillians, gods, trained martial artists and Wesker?
  - If you know what you're doing, he's quite the Badass.
Kamen Rider Ryuki as well as Ryu Terui from Kamen Rider Double.
Ryuuji Takasu from Toradora!, in which the whole premise of the title involves the concept of Tigers and Dragon's in Eastern Culture being seen as counterparts. 'Tora' is the Japanese word for tiger, while 'Dora' comes from 'Doragon' the japanese pronunciation of the English word 'Dragon'. The characters names in the show are the reverse of the title, Ryuji's name deriving from Ryu, the Japanese word for dragon, and the female protagonist/love interest is named Taiga Aisaka, 'Taiga' being the Japanese pronunciation of the English word 'Tiger'.
While not their proper names (being their hero names instead), the three protagonists of Madan Senki Ryukendo fit the bill.
Ryuu Tendou from Choujin Sentai Jetman. A non-Red example can be seen in Ryuu Hoshikawa in Kagaku Sentai Dynaman or to a smaller extent, Ryuunosuke Ikenami from Samurai Sentai Shinkenger and Ryuji Iwasaki from Tokumei Sentai Go-Busters. Then there's the RyuuRanger, Ryou of the Heaven Fire Star from Gosei Sentai Dairanger, another Red and dragon-themed.
Michael (known as Ryuuto in Japanese) of Pok�mon XD: Gale of Darkness is a subversion; the proper translation is "to kill".
Peacemaker Kurogane has Ichimura Tatsunosuke (where "Tatsu" is the character for the Eastern Zodiac sign of the dragon) and the Historical Domain Character Sakamoto Ryoma, whose name is written with the characters for "dragon" and "horse", and who fits the trope quite well.
Ryuuzaki (one of the aliases of Hero Antagonist L) from Death Note fits all the requirements except the "outgoing personality" bit (and according to Word Of God his alignment is questionable) but he's a good fighter, trained in Capoeira, he hates injustice with a passion, and has a rivalry with Light/Kira of the obvious Red Oni, Blue Oni type. There's also the Shinigami Ryuk and the OTHER Ryuuzaki from Another Note but they are subversions, one being an amoral monster and the other a Serial Killer.
Ryuuma from Eiichiro Oda's one-shot Monsters fits all requirements to some degree. His later appearance in One Piece - not so much. Justified in that he got Brook's personality and is revived as an evil zombie.
Ryuuta Ippongi from Osu! Tatakae! Ouendan fits this almost perfectly.
Ryugamine Mikado from Durarara!!, minus the outgoing personality and fighting skills (although he started working on that in the light novels).
"Wooden Sword" Ryuu of Shaman King, having all but a clear rivalry with a tiger themed character. Instead, his partner spirit has (or, had) a rivalry with the main character's partner.
Ryuuji Kisaragi of Dragon Crisis.
In Mobile Suit Gundam, we have Ryu Jose. Though he's not the protagonist, he is the most skilled pilot of the crew in the beginning, is the most likeable, big brother type, and sacrifices himself to save his crew. His death is a large reason that the crew shape up and start working together better.
- In Gundam Sentinel, the protagonist's name is Ryu Roots.
Kusuha Mizuha and Brooklyn "Bullet" Luckfield of the Super Robot Wars Alpha timeline are considered the mains of the series. Their ultimate robot? RyuuKoOu.
Ryuuichi and Ryuuji, recurring antagonists from the Kunio Kun series. Their names can be read as "dragon one" and "dragon two," and they are indeed Expys of the Double Dragon protagonists (though their Dub Name Change in River City Ransom somewhat obscured this). Toraichi and Toraji are presumably their "tiger" counterparts, but they never appeared in the same game.
Tatsumaru, Rikimaru's brother in the Tenchu series.
A somewhat ambiguous case, but Ryuuho Tairen of sCRYed is nominally one of the protagonists of the series, along with Kazuma. His father Ryuu is a pretty decent guy, too.
Ironically subverted with Gatchaman. While there IS a Ryu on their team, he's the Big Guy. And the person who fits the model of being the "Ryu" of that team (protagonist dressed in white) is actually named Ken. And the "Ken" of the team is named Joe.
Ryu from Chojin Sentai Jetman.