RyuTai

RyuTai is the het ship between Ryuuji Takasu and Taiga Aisaka from the Toradora! fandom.

Canon
In the begging of the series, their relationship starts off as an mix up, accidental, love letter confession on Taiga's part. After Taiga breaks into Ryuuji's home to retrieve the letter, he appeases here saying that he has written many embarrassing love letters his crush (Minori). Knowing about each others crushes, they decide to work together as matchmakers to each other. Here, is where their relationship kicks off.

For the next couple episode, they create crazy plans to try and pair each other up with their crushes. However, many of these plans fail miserably. As an example of this, Taiga plans to give cookies to her crush (Yusaku). Just when she is about to give them to Yusaku, she trips on the stairs and all the cookies end up breaking. Ryuuji comforts Taiga after this, saying the cookies tasted great and he is sure Yusaku would have loved them.

During the series, Ryuuji acts as a caretaker towards Taiga, as she lives on her own but does not know how to cook nor clean. Ryuuji usually makes breakfast, lunch, and dinner for the two of them. Ryuuji also cleans up Taiga's house when it starts to get messy. Ami points out this fatherly behavior when confronting Ryuuji's feelings about Taiga, saying he should stop treating her like a daughter and more like a partner/lover.

Taiga does appreciate the things Ryuuji does for her, but has a hard time putting her thoughts into words. Taiga does try to do this, especially when she realizes her feelings for Ryuuji in the Christmas Special episode. In this episode she ends up celebrating Christmas alone after preforming at the Christmas party at the school. Ryuuji notices her sudden absence, and decides to go visit her at her home dressed as a bear version of Santa. When he arrives, he plays as Santa before Taiga rips off his bear mask telling him to confess to Minori before its to late. Ryuuji leaves, and immediately after this Taiga realizes her feeling for him. She bursts into tears, knowing how much she depends on him,

Fanon
The RyuTai ship is by far the most popular ship in the fanbase. Not only because of the cute and wholesome dynamic of the ship, but also it being the main relationship in the series.