The rise of popularity to Bakugo post-Character Development caused him to be shipped with several characters, many of which he has little to no interactions with, Bakugo/Tsuyu and Bakugo/Toga being the most prominent among them, especially for the fact these characters rarely, if ever, appeared even in the same page on the comic, let alone having had any relevant interactions.
Midoriya's great status as a Launcher of a Thousand Ships causes him to be very much prone to take part in these. Being the protagonist, he gets the bulk of being shipped with the resident Ms. Fanservices Midnight and Mt. Lady in erotic works. While he showed interest in them, with him commenting on the latter's sexiness, it was entirely out of curiosity for their hero status and he has little interactions with either.
Midoriya/Ashido which gathered a following in Reddit, in spite of the fact they had about two conversations in the manga. This might be because they both share similar heroic ideals.
Midoriya/Dabi is a particularly rare case in which not only have neither of those characters ever interacted with each other prior to Chapter 293, but Female Midoriya/Dabi is more popular than regular male Midoriya among shippers.
Despite not having appeared together yet, being aquatic mammal themed heroes, Selkie and Gang Orca are shipped sometimes.
Kaminari/Shinso can be seen as this. Having a following on Tumblr and Instagram, this ship was given birth during the Joint Training Arc, despite Kaminari only talking to him to befriend him twice, never mind the fact that Kaminari is canonically heterosexual. It can also be a case of Pair the Spares by Yaoyorouzu/Jiro shippers.
Doubling with Toy Ship, Eri/Kota, who have never met, are shipped due to them being in the same age group and their admiration of Midoriya.
Bakugo/Yaoyorozu have rarely interacted, but they have a noticeable, if small, fandom with considerable amounts of fanart. Some people like the idea of a Bad Boy/Ojou ship. To the ship's credit, their interaction in Smash!! was laced with Ship Tease when Bakugo held Yaoyorozu hostage and under the effects of a Bishōnen Quirk, hits on her. And they were drawn in an outfit swap together.
There are some fans who ship Hawks/Fuyumi, if only to watch Endeavor's reaction, even if they've never actually met face-to-face. Comparisons to the infamous scene in 22 Jump Street are often raised.
Iida/Camie has amassed a small, but devoted fanbase despite having no interaction at all. Their contrasting personalities and styles of speaking may have contributed towards it.
The Joint Training arc not only boosted Class 1-B in popularity, but also in pairing with their 1-A colleagues as well, even though this is the only arc besides the trainning camp and War arcs where all students interact directly.
Setsuna Tokage is mostly paired with Midoriya (no surprise there), Bakugo (due to their competitive nature), Ashido (due to their teasing personalities), Kaminari and Hanta.
Itsuka Kendo is often paired with Midoriya, Uraraka and Yaoyorozu. Sometimes all at the same time.
Pony Tsunotori is often paired with Midoriya (due to their Badass Adorable looks), Shoji, Asui (due to being amongst the few heteromorphs in their respective classes) and Todoroki (since she was carrying him bridal-style after he was defeated during their match.)
Yui Kodai has become a popular pair to Midoriya and Uraraka, specially since she is, technically a Retool from Uraraka's original design.
Ibara Shiozaki is often paired with Kaminari, since they interacted twice (first during the Sports Festival, then during their Joint Training match) and fans think her stoic personality serves as a good contrast to his laidback one. Bakugo has also become a pairing to her as well, as part of helping him on his redemption arc into a better person.
Dabi/Overhaul is fairly popular on AO3, even though the two characters have never interacted with each other. Fanworks tend to emphasize Overhaul's uptight personality and typically heavily focus on Dabi irritating him on purpose. Presumably, the contrast of Overhaul's cleanliness obsession with Dabi's grungy, borderline-punk aesthetic is part of the appeal.
The most popular pairing for Todoroki's brother Natsuo is Shigaraki, despite how the two of them have never met. It's a popular side ship in Dabihawks works, possibly as a Pair the Spares. Fans of this ship focus on Natsuo's poor relationship with his dad and have him and Shigaraki bond over their cynicism towards hero society.
