Baka and Test/WMG

Hideyoshi's parents are filthy rich and want to keep his real gender a secret.
It would certainly explain why he he has his own changing room and own area in a public bath, and a rather classy-looking one at that.

Hideyoshi is actually a girl, who happens to be quite the Tomboy and has deluded herself into thinking she is a male.
Well, the title explains everything.
 * Or Hideyoshi is transgendered.

Hideyoshi is the historical Toyotomi Hideyoshi when he was young. He went to ~400 years ago after the story.
And what's more, Hideyoshi is an artificial hermaphrodite and is infertile. This explains why the historical conqueror nevered had a kid before he became old. That two sons he had later must be result of one of his concubines cheating on him.

Hideyoshi is going to get a full-on shirtless scene near the end of the series, whenever that is. And possibly a super manly one at that.
...Because Rule of Funny.
 * Actually, more like the first episode of season 2.

Himeji is related in some way to Yuuji's mother.
In Yuuji's background episode, we see Yuuji's mother, who is extremely similar to Himeji in both personality and physical appearance. She's even just as bad at cooking as Himeji.

Akihisa will lose it someday.
While, granted, some of the horrible things that happen to him are FUNNY, and some are due to his own "ahem" lack of intelligence, I have a feeling that he will snap sometime soon. And I don't know why, but I have a feeling his desire to leave them will somehow raise his grade.

Akihisa isn't actually Oblivious to Love.
It's just that due to his Acquired Poison Immunity, there is a chance that he will turn into a Poisonous Person, which, quite honestly would definitely make his love life made of suck. I said "he will" because.

Himeji is actually Irisu Kyouko's long-lost sister.
That explains the Yandere tendencies and similar interest in bunnies... Also, they look really similar. Compare this to this. The more you know...

Himeji is actually Yuno's daughter...from the future!!!
Or her lost twin sister...from the future!!!

Kaoru Toudou was involved with Academy City.
The Shoukanjuu Summoning System was an accidental combination of science and a supernatural power, and the catchphrase of the Index series is "When magic and science collide... the story begins!" And with the existence of that reality-warping studio from Railgun Episode 13, this only furthers my point.