Tareme Eyes

A style in Anime and Manga of drawing eyes where they droop or sag. It is the usual way you'll see eyes on a Moe character. It generally represents a kind, quiet or otherwise soft person. Only really notable if there are more than a handful of characters that are drawn without them.

This does not, however, mean that Tareme Eyes are Always Lawful Good Eyes. In real life, eyes visually take a downward droop when someone is looking down on you, and looking calm in a tense situation is an affirmatively Badass trait.

Note that the "me" in "tareme" actually means "eyes" in Japanese. We just enjoy being redundant.

Its opposite is Tsurime Eyes.

Examples

This is an East Asian media only trope. Please do not put Western examples here.

Anime and Manga

(Shown above) Tsukasa Hiiragi, from Lucky Star. Interestingly, her diametrically different twin sister, Kagami, is a good example of Tsurime Eyes. Miyuki, Hiyori, and almost every other character in the Lucky Star cast are also Tareme.
- In the earlier manga episodes, Konata was Tareme.
Mikuru Asahina, the Moe Blob of Suzumiya Haruhi.
- Alt!Yuki from The Disappearance of Haruhi Suzumiya, unlike the regular Yuki Nagato.
No small number of characters from CLAMP works, due to the overwhelming amount of kind-hearted, gentle characters.
Haruka Nogizaka, (who looks suspiciously similar to Mikuru) the main (and very moe) character of Nogizaka Haruka no Himitsu.
Orihime Inoue, the healer from Bleach. Also, Ururu, Retsu, Momo, and Hanataro. Possibly subverted by Yachiru.
- And don't forget sweet, lovable Captain Aizen pre-reveal.
Subverted with Sayoko of Ah My Goddess: she sports Tareme, but she's not all that nice.
Tsubaki, the Yamato Nadeshiko of Soul Eater.
- Also Chrona, the Woobie.
Saya from Blood Plus.
Mikan Sakura, the Cloudcuckoolander of Gakuen Alice.
In Fairy Tail, Natsu Dragneel and Gray Fullbuster make a point of insulting each other with names derived by the others' eye shape. Gray is Tareme while Natsu is Tsurime. "Droopy-eyed bastard!!"
Osaka, the Cloudcuckoolander from Azumanga Daioh. She also has the same seiyuu as fellow cuckoolander Orihime above.
Tsumugi Kotobuki and the Hirasawa sisters of K-On!
Yugi Muto of Yu-Gi-Oh. (Unlike the pharaoh who has Tsurime Eyes)
Kanako Oora and Shouko Maruuchi from Sayonara Zetsubou Sensei has these kinda eyes.
Himeko Kurusegawa of Kannazuki no Miko, who is countered by Chikane's Tsurime Eyes. Both are used more liberally in the mangas).
Male Example: Takeru from Digimon Adventure 01. His brother, Yamato, on the other hand...
Rena, Hanyuu, Rika and Satoshi from Higurashi no Naku Koro Ni.
- Miyo has the adult (i.e. smaller) variety, which gives her a somewhat spaced out expression. Hence the name "Droopy-tan."
  - Most of these are massive subversions: Rena and Satoshi have both gone into murderous Ax Crazy freakouts, and Takano Miyo is actually the villain. However, they truly are very nice, and cute.. Even Miyo, to a point.
In-universe, characters refer to Sanzo from Saiyuki as being droopy-eyed. This is important his character development, it belies his genuinely caring nature.
Classic Moe character Ami Mizuno/Sailor Mercury from Sailor Moon has a noticeable case, especially when compared to Rei, who has Tsurime Eyes and Tsundere tendencies.
Katekyo Hitman Reborn - Male examples: Tsuna, Basil, Ginger Bread, and Fuuta. Female examples: Kyoko, Haru, Chrome, Nana (Tsuna's mother), and Uni.
Fullmetal Alchemist's Alphonse Elric. Well, when he was human at least.
- He eventually does get his body back, cute puppy-dog eyes and all.
A lot of characters in Mahou Sensei Negima, especially Konoka and Sayo.
- Also Zazie, which is important because it's one of the few ways of distinguishing her from her sister.
- Negi's eyes are this normally....but when he gets pissed or enters Dark Mode?
In Fairy Tail, one of the insults Natsu throws at his guild rival Gray is "tareme," translated as "droopy eyed." Even when he is angry (which he often is around Natsu) his eyes never cross the "straight" threshold.
Lucy's more innocent "Nyu" personality and Nana have these in Elfen Lied. Subverted with Creepy Child Mariko though.
Yui from Angel Beats is the only female character that you see regularly with tareme eyes.
- The bassist and drummer of GDM have them also, but they get very little screen time comparatively.
Ryoko from Aoi Hana has them, likely to underline her well-natured, motherly persona.
The eponymous character of Hikaru no Go has this kind of eyes, in contrast to his rival Akira's Tsurime Eyes. It serves to underscore his easygoing nature as opposed to Akira's seriousness, at least early on.
Yura from Futari Ecchi has Tareme eyes, which she inherited (together with big boobs) from her mother, unlike her younger sister Rika.
Asuka from Future GPX Cyber Formula, contrasting Miki's Tsurime Eyes.
Pre-Time Skip Simon in Gurren Lagann, which only contribute to his downright adorable smile.
Finland in Axis Powers Hetalia, compared to the other Nordics.
Puella Magi Madoka Magica has both the best friends Madoka and Sayaka.
Essentially every main character in Wandering Son.
Fran from Franken Fran. Honestly, you don't expect someone with those kind of distant, sleepy eyes to be capable of the things she's done.
Outer Moka from Rosario to Vampire sports these, as opposed to Inner Moka.
Kazemakase Tsukikage Ran: Used with the cute Meow and any Yamato Nadeshiko she runs into.
An interesting example from Get Backers; cheerful, affectionate Ginji Amano has wide, bright tareme, in contrast to his partner Ban's Tsurime. But when Ginji's Lightning Emperor persona awakens, his eyes become narrow, dark, and markedly Tsurime.
Windaria Marie's eyes are noticably rounder and more down pointed than Veronica's or Selenia's.
In The World God Only Knows, Keima mentions these as one of the reasons the heroine from a galge is his soul mate.
The Son males (Goku, Gohan and Goten) from Dragonball Z sport this eyes, a show that they're the nicest people around. When they get pissed though (And consequentially transform into Super Saiyans) their eyes change into a pupilless Tsurime.
Pokémon Special has Diamond of the DP trio.
Several characters in Sora no Otoshimono feature these type of eyes, most notably Chaos. However she does not follow the typical archetype. Atleast not at first.

Video Games

Many young characters in the Dept Heaven series have eyes drawn like this, although it's restricted to the very young knights in Knights in The Nightmare (and Pisce).
- This is rather amusing in Riviera the Promised Land, where the Tsundere of the cast is drawn with tareme and the good-natured Tomboy with tsurime.
Pretty much the entire cast of Star Ocean: First Departure.
The title character of Um Jammer Lammy.
The Touhou Project has Satori Komeiji, whose eyes are extremely droopy; enough to look at least half-closed. In the games, this actually serves to give her more of a bored look than a cute one (Her illustration in the Grimoire of Marisa plays it for cute, though).
Crowe Brust from The 2nd Super Robot Wars Z.