My Hero Academia

My Hero Academia is an ongoing manga by Kōhei Horikoshi. It got an anime adaptation with two full seasons so far. The third season is currently being released.

Plot
On an Earth-like world where people with superpowers known as "Quirks" are the norm, Izuku Midoriya is a regular middle school student who has dreams of one day becoming a Hero despite being bullied by his classmates for not having a Quirk. After being the only one to try and save his childhood bully Katsuki from a Villain, the world's greatest Hero All Might bestows upon him his own quirk "One For All". The story follows Izuku's entrance into U.A. High School, a school that cultivates the next generation of Super-Heroes.

Het

 * YoseMomo - the ship between Yosetsu Awase and Momo Yaoyorozu
 * IzuOcha - the ship between Izuku Midoriya and Ochaco Uraraka
 * MidoTsuyu - the ship between Izuku Midoriya and Tsuyu Asui
 * IzuMina - the ship between Izuku Midoriya and Mina Ashido
 * IzuMei - the ship between Izuku Midoriya and Mei Hatsume
 * Iidaraka - the ship between Tenya Iida and Ochaco Uraraka
 * TogaDeku - the ship between Izuku Midoriya and Himiko Toga
 * Kacchako - the ship between Katsuki Bakugou and Ochaco Uraraka
 * Katsuyu - the ship between Katsuki Bakugou and Tsuyu Asui
 * BakuToga- the ship between Katsuki Bakugou and Himiko Toga
 * BakuMomo - the ship between Katsuki Bakugou and Momo Yaoyorozu
 * BakuMina - the ship between Katsuki Bakugou and Mina Ashido
 * GrapeAcid - the ship between Minoru Mineta and Mina Ashido
 * GrapeCreate - the ship between Minoru Mineta and Momo Yaoyorozu
 * GrapeGravity - the ship between Minoru Mineta and Ochaco Uraraka
 * GrapeFrog - the ship between Minoru Mineta and Tsuyu Asui
 * GrapeInvisiblity - the ship between Minoru Mineta and Toru Hagakure
 * GrapeSound - the ship between Minoru Mineta and Kyoka Jiro
 * IidaOcha - the ship between Ochaco Uraraka and Tenya Iida
 * KiriMina - the ship between Eijiro Kirishima and Mina Ashido
 * SeroMina - the ship between Hanta Sero and Mina Ashido
 * TodoMomo - the ship between Shouto Todoroki and Momo Yaoyorozu
 * TokoTsuyu - the ship between Tsuyu Asui and Fumikage Tokoyami
 * OjiTooru - the ship between Tooru Hagakure and Mashirao Ojiro
 * KamiJirou - the ship between Kyoka Jirou and Denki Kaminari
 * Kyoji - the ship between Kyoka Jiro and Kijo Koda
 * FumiMina - the ship between Fumikage Tokoyami and Mina Ashido
 * MinaYama - the ship between Mina Ashido and Yuga Aoyama
 * ShojiKure - the ship between Mezo Shoji and Toru Hagakure
 * AusiKoda - the ship between Tsuyu Asui and Koji Koda
 * SatoToru - the ship between Rikido Sato and Toru Hagakure
 * EraseMidnight - the ship between Shota Aizawa and Nemuri Kayama
 * TetsuKendo - the ship between Tetsutetsu Tetsutetsu and Itsuka Kendo
 * KenMono - the ship between Itsuka Kendo and Neito Monoma

Slash

 * DekuHead - the ship between Shota Aizawa and Izuku Midoriya
 * BakuDeku - the ship between Izuku Midoriya and Katsuki Bakugou
 * KiriDeku - the ship between Ejiro Kirishima and Izuku Midoriya
 * IidaDeku - the ship between Izuku Midoriya and Tenya Iida
 * TodoDeku - the ship between Izuku Midoriya and Shouto Todoroki
 * ShigaDeku - the ship between Izuku Midoriya and Tomura Shigaraki
 * TodoBaku - the ship between Katsuki Bakugou and Shouto Todoroki
 * KamiBaku - the ship between Denki Kaminari and Katsuki Bakugou
 * KiriBaku - the ship between Katsuki Bakugou and Eijiro Kirishima
 * TodoDenki - the ship between Shouto Todoroki and Denki Kaminari
 * EraserMight - the ship between Toshinori Yagi and Shota Aizawa
 * KiriDenki - the ship between Eijiro Kirishima and Denki Kaminari
 * EraserMic - the ship between Shota Aizawa and Hizashi Yamada
 * KamiSero - the ship between Denki Kaminari and Hanta Sero
 * KiriSero - the ship between Eijiro Kirishima and Hanta Sero
 * MiriTama - the ship between Mirio Togata and Tamaki Amajiki
 * IidaSho - the ship between Tenya Iida and Hitoshi Shinso
 * ShinsoDeku - the ship between Hitoshi Shinso and Izuku Midoriya
 * BakuShinso - the ship between Katsuki Bakugou and Hitoshi Shinso
 * SatoGou - the ship between Rikido Sato and Katsuki Bakugou
 * IzuMezo - the ship between Izuku Midoriya and Mezo Shoji
 * OjiYama - the ship between Mashirao Ojiro and Yuga Aoyama
 * SeroBaku - the ship between Hanta Sero and Katsuki Bakugou
 * SeroDeku - the ship between Hanta Sero and Izuku Midoirya
 * KamiYama - the ship between Denki Kaminari and Yuga Aoyama
 * TetsuKami - the ship between Denki Kaminari and Tetsutetsu Tetsutetsu
 * ShinOji - the ship between Hitoshi Shinso and Mashirao Ojiro
 * TokoShoji - the ship between Mezo Shoji and Fumikage Tokoyami
 * TodoKami - the ship between Shoto Todoroki and Denki Kaminari
 * MiriDeku - the ship between Mirio Togata and Izuku Midoriya
 * KiriTama - the ship between Eijiro Kirishima and Tamaki Amajiki
 * MonoBaku - the ship between Neito Monoma and Katsuki Bakugou
 * ShishiKami - the ship between Seiji Shishikura and Denki Kaminari
 * InaTodo - the ship between Inasa Yoarashi and Shoto Todoroki
 * Seroroki - the ship between Hanta Sero and Shoto Todoroki
 * KiriTetsu - the ship between Eijiro Kirishima and Tetsutetsu Tetsutetsu

Femslash

 * Tsuchako - the ship between Ochaco Uraraka and Tsuyu Asui
 * OchaMina - the ship between Ochaco Uraraka and Mina Ashido
 * MinaTsuyu - the ship between Tsuyu Asui and Mina Ashido
 * TogaTsuyu - the ship between Tsuyu Asui and Himiko Toga
 * MomoJirou - the ship between Momo Yaoyorozu and Kyouka Jirou
 * ToruMina - the ship between Toru Hagakure and Mina Ashido
 * JiroMina - the ship between Kyoka Jirou and Mina Ashido
 * OchaMomo - the ship between Ochaco Uraraka and Momo Yaoyorozu
 * MomoNight - the ship between Momo Yaoyorozu and Nemuri Kayama
 * AsuiKure - the ship between Tsuyu Asui and Toru Hagakure
 * NightAcid - the ship between Nemuri Kayama and Mina Ashido
 * KendoMomo - the ship between Itsuka Kendo and Momo Yaoyorozu

Polyship

 * ShinTodoBakuDeku - the ship between Hitoshi Shinso, Shoto Todoroki, Katsuki Bakugou and Izuku Midoriya
 * TodoBakuKiriDeku - the ship between Shoto Todoroki, Katsuki Bakugou, Eijiro Kirishima, and Izuku Midoriya
 * TodoBakuDeku - the ship between Shouto Todoroki, Katsuki Bakugou, and Izuku Midoriya
 * KiriBakuDenki - the ship between Eijiro Kirishima, Katsuki Bakugou, and Denki Kaminari
 * KiriBakuDeku - the ship between Eijiro Kirishima, Katsuki Bakugou, and Izuku Midoriya
 * SeroMinaYama - the ship between Hanta Sero, Mina Ashido, and Yuga Aoyama.
 * IzuOchaIida - the ship between Izuku Midoriya, Ochaco Uraraka, and Tenya Iida
 * Yagmazawa - the ship between Toshinori Yaga, Hizashi Yamada, and Shota Aizawa
 * KiriSeroDenki - the ship between Eijiro Kirishima, Hanta Sero, and Denki Kaminari
 * TodoIiDeku - the ship between Shouto Todoroki, Tenya Iida, and Izuku Midoriya

Friendship

 * Dekusquad - the friendship between Izuku Midoriya, Tenya Iida, Ochaco Uraraka, Shoto Todoroki, and Tsuyu Asui
 * Bakusquad - the friendship between Katsuki Bakugo, Eijiro Kirishima, Denki Kaminari, Hanta Sero, and Mina Ashido

Cargo

 * GrapeAcid 2.0 - the ship between Mineta and the drug
 * GrapeGrape - the ship between Mineta and a literal grape
 * Katsudon - the ship between Izuku Midoriya and a delicious pork cutlet bowl
 * GrapeStrawberry - the ship between Minoru Mineta and Kaori Neo
 * No Mineta - the ship between Mineta and him being erased from existence

Fanon
My Hero Academia's most dominant ships in popularity are TodoDeku and KiriBaku.