Kind Red Eyes

You see a character with red eyes. He's going to be violent or menacing, right? Wrong. On the contrary, his red gaze is one of the most comforting features of his face, because he has Kind Red Eyes.

Crimson gems of benevolence and nobility.

Traditionally, red eyes have been a negative feature, showing a character's evil or villainy. But as tropes mature and become subverted and averted, you see more characters whose red eyes have no negative connotation whatsoever. They can even be a Fetish Fuel.

Kind Red Eyes could belong to a Heroic Albino, but just as often they belong to a Friendly Neighborhood Vampire, or may even be a literally Red Herring. Sometimes they're just pretty, or colorful, and don't have any relevance to the story.

A subtrope of Technicolor Eyes. Contrast Red Eyes, Take Warning, with which it can occasionally overlap (especially if a character is a Tsundere or Badass). In short, the character's eyes may be red, but their eye color's lack of villainous connotation is played absolutely straight. If the character is a Redheaded Hero, expect Curtains Match the Window.

There are two types of these:

The perfectly played straight trope, where characters with red eyes have never been, are never seen on screen and will never be seen as dangerous.
The downplayed trope. A character with red eyes is usually well intended, good hearted and so on, but in certain circumstances, they can become angry or dangerous. Beware the Nice Ones, indeed. Subversions, inversions included.

Examples of Kind Red Eyes include:

Type 1

Anime and Manga

Ion Fortuna in Trinity Blood. Just look at them...
Cheza in Wolf's Rain.
Fate Testarossa from Magical Girl Lyrical Nanoha.
Iczer-1 and Iczer-3 in the Iczer series (Iczer-3's eyes are actually orange, but I'd say they count for this).
Hikaru in Magic Knight Rayearth.
Chibiusa in Sailor Moon is probably one of the first examples of this, as is Sailor Pluto. Luna has red eyes in cat form. Princess Kakyuu has red eyes to match her "fire" theme. Sailor Mars has red eyes in some promotional art, mostly in images where the senshi are Colour-Coded for Your Convenience.
Sakura from Tokko.
The Ishvalan people in Fullmetal Alchemist, the ones that try to be pacifist anyway.
Takato Matsuda in Digimon Tamers has red eyes and is perhaps the most innocent of the original three tamers in the series, wanting nothing more than to spend his days playing with his partner, Guilmon.
In Samurai 7, the kind and patient priestess Kirara has red eyes, as does her equally nice (if Bratty Half-Pint) sister Komachi. This might actually be a racial trait, as the villagers in general tend to have reddish brown eyes.
The titular character of Puella Magi Madoka Magica has them, though official art makes them more pink-ish.
Ichigo Hoshimiya in Aikatsu!.

Video Games

Impa and Sheik from Ocarina Of Time.
The Crimson Eyed Tribe from Eternal Eyes.
Ninian and Nils in Fire Emblem Elibe.

Type 2

Anime and Manga

Saya in Blood Plus. Though as an Action Girl Friendly Neighborhood Vampire, she also has some Red Eyes, Take Warning moments. Curiously, her Evil Twin has sinister Blue Eyes.
The first Ishvalan in Fullmetal Alchemist we see is Scar, whose red eyes are at first seen as Red Eyes, Take Warning.
Lina Inverse sits on the fence between this trope and Red Eyes, Take Warning, given she is a Fiery Redhead Person of Mass Destruction, but nevertheless a Jerk with a Heart of Gold.
Reinforce, Lutecia and Deed in Magical Girl Lyrical Nanoha after their respective Heel Face Turns. Wendi, while not a bad sort, may be too mischievous to really fit.
Seras from Hellsing. In the anime she has red eyes for the entirety of the show, and is easily the most morally upstanding character.
Mayura; resident Muggle in Mythical Detective Loki Ragnarok and Ecchan; harmless Team Pet.
Possible inversion, but Kaworu Nagisa from Neon Genesis Evangelion has a very warm, comforting gaze. Even though he winds up being the enemy... Or does he?
- Actually, this trope would fit Rei Ayanami even better, considering... well, everything.
  - GNR and the army of Naked Reis make the look of kindness into a very serene Slasher Smile, considering what they're doing.
Van of Gun X Sword has eyes of a very distinctive red-brown color. Although he has been known to terrify an enemy with a single look, the color of his eyes is probably least noticeable when he's full of rage. On the contrary, a focus on his eyes that highlights their color often means that he's worried about or feeling sympathetic towards someone.
Holo from Spice and Wolf, at least in human form, comes across as benevolent and adorable most of the time. The only time her eye color is emphasized it's used an an indication of extreme emotional vulnerability rather than outright danger.
Kamina from Tengen Toppa Gurren Lagann is really a kind-hearted and easygoing person at the core, underneath his loud-mouthed, ridiculously reckless persona.
Ruby has these in Pokémon Special, but he does occasionally have Red Eyes, Take Warning when he stops Obfuscating Stupidity.
- Also some of the Pokemon themselves.
Saki is this most of the time, but when she plays mahjong her phenomenal skill transforms her into Red Eyes, Take Warning.
In Sayonara, Zetsubou-sensei, the genki, ultra-optimistic Kafuka and Kiri, the friendly hikikomori both have eyes which depending on the scene are reddish brown or blood red. Although, given that Kafuka's actually a yangire, she's also Red Eyes, Take Warning.
Ghost in the Shell gives us Major Motoko Kusanagi. Sometimes.
Yukino from Kare Kano.
Kurenai Yuuhi of Naruto has deep red eyes but has a very pleasant character (which is not to say she isn't Badass}. In the same show we have the Uchiha, who possess the Sharingan dojutsu and most of which we see become Ax Crazy because someone had their whole clan killed.
Kyubey of Puella Magi Madoka Magica is of the... other variety.

Comic Books

The Martian Manhunter is often depicted with red eyes, and he's the soul of the team.
- Miss Martian has the same thing going for her, being a Distaff Counterpart to the Manhunter from Mars.
Gambit, kinda...
Sleepwalker's eyes are a subversion in that most people are freaked out by them, although that may be because they're compounded like an insect's. A few people, such as Pike and Alyssa Conover, are able to look deeper and see the kindness within them.

Fan Works

Hanae Mitsukawa in Pretty Cure Perfume Preppy has red eyes in civilian form, but she's a shy and fragile Meganekko. When she becomes Cure Tangerine, her eyes turn orange to match her theme color.
Ogata Mia from Futari wa Pretty Cure Blue Moon, though she starts out as an obstacle to the Cures, is a sweet red-eyed girl who becomes a friend and member of the core team even if she doesn't fight. Dawn also counts; although she's powerful and intimidating, she's a good guy. Since the story goes with the Pretty Cure tradition of Earth natives having matching hair and eyes, the only red-haired character without red eyes is Kainatrol, easily the most evil character.
Like his Earth-616 counterpart, Ultimate Sleepwalker's glow a bright red. Some of the people Sleepwalker has helped out and who've gotten a good look at his eyes often feel strangely reassured by them, even when they know they should be scared.

Literature

In James Swallow's Warhammer 40000 Blood Angels novel Black Tide, Kilian's eyes are commented on as dark red -- shortly after he has helped saved the lives of Rafen, Tarikus, and Vetch.
Skybaxes in Dinotopia usually have yellow or red eyes. This trope is perhaps best exemplified by this fanart.
In Pretties (of the Uglies series), Shay actually HAS RUBIES IN HER EYES.
Hestia from the Percy Jackson and The Olympians books literally has eyes of fire, but they have the effect of a cozy fireplace.

Video Games

The Female Main Character in the PSP version of Persona 3 has them, and she actually has a much warmer, positive demeanor than her male counterpart.
Tifa Lockhart from Final Fantasy VII fits this trope like a glove.
Anissa, the farmer's daughter in Harvest Moon: Tree of Tranquility and Animal Parade.
Peppy Hare and his daughter Lucy Hare in the Star Fox series.
Russell, a general forced to work for the enemy by extenuating circumstances and all too happy to make a Heel Face Turn, in Yggdra Union.
Dizzy from Guilty Gear, who while powerful, is arguably the nicest person in the entire game.
Azusa and Takane are the only characters in The iDOLM@STER to have red or pinkish eyes. Azusa is a ditzy big sister type, and while Takane starts off as a rival she's shown to be incredibly polite.
In Rune Factory 2, Dorothy tends to hide these under Blinding Bangs. The player will only be able to see her eyes at her wedding.
Himi of Yamatai in Golden Sun Dark Dawn, a mild-mannered Shrine Maiden.

Webcomics

Zimmy from Gunnerkrigg Court is an interesting example. Usually her eyes are obscured by black goo, and she is usually unstable and highly abrasive. When the goo clears up her eyes are visibly red, and this is when she is at her most happy, stable and nice to be around.
Dave Strider from Homestuck recently turned out to have bright red eyes beneath his signature shades. According to Karkat, he hides them under his shades due to being insecure about his eyes - His friends have the relatively normal eye colors of green and blue, and Rose has purple eyes, which are rare but not unnatural like red.
Buwaro from Slightly Damned is the absolute embodiment of this trope. I mean, just look at those big, cute, blood-red puppy-dog eyes!

Western Animation

A few of the titular characters in My Little Pony. No, despite what some cynical websites will tell you; they aren't demonic.
Sari Sumdac of Transformers Animated. This changes when she discovers she's techno-organic and upgrades herself using her key. From then on, her eyes are blue like other Autobots, although in her "human Mode" the different shades of blue are flipped around.
- The Maximals from Beast Wars.
Actually subverted and turned into an example of Red Eyes, Take Warning with the villains of the ice-skating episode of Tuff Puppy.