My Hero Academia

My Hero Academia is an ongoing manga by Kōhei Horikoshi. It got an anime adaptation with two seasons so far.

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
 * Katsudon - the ship between Izuku Midoriya and a delicious pork cutlet bowl
 * 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
 * GrapeStrawberry - the ship between Minoru Mineta and Kaori Neo
 * IidaOcha - the ship between Ochaco Uraraka and Tenya Iida
 * KiriMina - the ship between Eijiro Kirishima and Mina Ashido
 * Serashido - 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

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
 * Izuzo - the ship between Izuku Midoriya and Mezo Shijo
 * 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

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
 * AshiJiro - 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
 * Hagashido - the ship between Toru Hagakure and Mina Ashido
 * NightAcid - the ship between Nemuri Kayama and Mina Ashido

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

Cargo

 * GrapeAcid 2.0 - the ship between Mineta and the drug
 * GrapeGrape - the ship between Mineta and a literal grape

Fanon
My Hero Academias most dominant ships in popularity are TodoDeku and KiriBaku.