Kaomoji

Kaomoji (顔文字) is the Japanese word for "face characters". Unlike Western emoticons :) which go sideways and have less detail, kaomoji can be understood without having to tilt your head (^_^).

AA characters such as Mona and Giko evolved from kaomoji. However, unlike AA, Kaomoji only take up one line and therefore do not need to limit themselves to certian fonts or character sets to be understood.

Notable Kaomoji

(╯°□°)╯︵ ┻━┻
(ノಥ益ಥ)ノ ┻━┻
(ノಠ益ಠ)ノ彡┻━┻
Represents someone flipping a table in anger.
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┬──┬ ¯\_(ツ)
┬─┬ノ( º _ ºノ)
Represents someone calmly putting said table back.
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uwu
owo
Represents a cat-like smile. It's associated with anime and the furry community.
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ಠ_ಠ
Represents a look of disapproval.
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West-Specific

( ͡° ͜ʖ ͡°)
( ‾ʖ̫‾)
Known as the "Lenny Face" or "deg deg". It used to be really big in 2012.
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ヽ༼ຈل͜ຈ༽ノ
Popularized by the League of Legends player Imaqtipie. Often accompanied by his catchphrase "Raise your dongers".
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ᕕ( ᐛ )ᕗ
Called "Happy Gary". He is just a happy guy that likes to dance.
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【=◈︿◈=】
Associated with the musician Porter Robinson, specifically his album Worlds.
Wikipedia

Japan-Specific

_(:3」∠)_
Represents a person lying down. It is sometimes called "Junsuke Takazawa".
Pixiv Encyclopedia

orz
Represents a person kneeling in despair.
KnowYourMeme2ch AA Illustration Project

\(^o^)/
This happy-looking emoticon, often paired with the phrase "My life is over", is ironically used to express profound despair.
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(((( ;゚Д゚)))ガクガクブルブル
Represents someone trembling in fear.
2ch AA Illustration Project

><
Associated with the phrase "わかんないんです><" / "I don't know ><". However, it's more likely to be used disingenuously than to communicate genuinely not knowing something.
2ch AA Illustration ProjectNico Nico Encyclopedia

<●><●>
"I know everything <●><●>". The opposite of ><.
2ch AA Illustration Project

ξ*゚⊿゚)ξ
ξ*〃〃)ξ
ξ#゚⊿゚)ξ
A tsundere emoticon, called "Tsun". She started out as Buun's girlfriend/childhood friend.
2ch AA Illustration Project

川 ゚ -゚)
川#゚ -゚)
A kuudere emoticon, called "Kuu".
2ch AA Illustration Project
Represents a miserable face. It's mostly used in China, but shows up in other countries. The character originally meant "window", but it's rarely used that way nowadays.
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Miscellaneous Kaomoji

These are just ones I think are cute, either made by me or stolen from somewhere.

Sources: