Suddenly a high school student Subaru Natsuki has been summoned to another world on the way back from the convenience store. With the biggest crisis of his life being summoned to another world and no sign of the one who summoned him things become worse when he is attacked. But when he is saved by a mysterious silver-haired girl with a fairy cat, Subaru co-operates with the girl to return the favor. When they finally manage to get a clue Subaru and the girl are attacked and killed by someone. Subaru then awakens in the place he was summoned and notices the ability he gained "Returns by Death" a helpless boy that only has the ability to rewind time by dying. And beyond the despair can he save the girl from the fate of death!. //Description from: jCafe, by Amario(?)

Every 30 years, a new princess is chosen from the Hime family to serve the Hayagami. The time has come again, but over these past years, records state not a single female has been born, save for one, the 15-year-old Arata. The only problem is, Arata is actually a male! Forced to disguise himself and take the place of the princess candidate until a formal one can be found, he attends the festival only to witness the current princess, Kokuri-hime, murdered, and his own life is forfeit as well, by the hands of the princess' personal guard, the 12 Shinshou. As he runs for his life, Kannagi of the 12 convinces everyone that Arata is the one who has murdered the princess instead, and now everyone in the Imperial Court is after his head! Now, another Arata from our world has crossed over in Arata's place! How did this happen, and how will these two survive?

From Viz:
Miaka Yuuki is an ordinary junior-high student who is suddenly whisked away into the world of a book, "The Universe of th Four Gods". There she becomes the priestess of the god Suzaku, and is charged with finding all seven of her Celestial-Warrior protectors.

Yui Kusanagi, is the daughter of a Shinto shrine. She discovers a mysterious sword, which transports her to a different world where she meets the Greek god Zeus. He invites her to attend a school in a separate world that he created. Zeus intends to teach the meaning of love to the various young divine beings who also attend the school, in an attempt to reverse the weakening bond between humans and the gods.

Note: The 3rd volume is an ebook only.

Mira peacefully resided in a magical world until a blow to the head caused her to partially remember her previous life in Japan. The protagonists in reincarnation stories always end up having to deal with trouble, which is the last thing she wants. Alas what awaited her was the selection exam for a magic academy and naturally her special cheat ability was discovered then.
A fantastical tale of a reincarnated girl who doesn't want any cheats.