If you're looking for anime similar to Vibe Kurui no Yuusha ga Arawareta! (Light Novel), you might like these titles.
While trying to protect a wooden relic, high school student Yuuri Mito summons the Goddess Kikuramikami no Hime in the form of a sweet, affectionate child; she begins to live with him, taking the name Mashiro. Yuuri promises to marry her when she grows up, which unfortunately for him happens overnight! However, they soon have bigger things to worry about, as the relic is accidentally destroyed, unleashing the Tayutai, a human-hating race of monsters. Along with Yuuri's childhood friend Ameri, his step-sister Yumina and Mifuyu - an honour student at Flawless Girls' Academy - Yuuri and Mashiro must step up to fight the Tayutai, protect the world, and even learn about underwear!
Self-proclaimed, proud pervert Ryousuke loves women – to him, their butts and breasts are a 'treasure box' of joy for all men. So when the boy spots a fiery-haired girl standing in the rain one day, he invites her to his house – but he didn't expect to be stabbed with a magical sword in return! The girl, Lisara, is actually a high-level shinigami who must absorb the spiritual powers of others to survive in the human world. Until she can find a genius with enormous expendable energy, she's decided to form a contract with Ryousuke, but unfortunately for the busty babe, the horny teen's mojo is fueled only through his constant perversion. While looking for Lisara's true prize, the two must deal with other well-endowed shinigami and other foes alike, all while trying to maintain a 'typical' school life together.
In the near future, monstrous creatures called “phantoms” descend upon the world. Haruhiko Ichijou is a student at Hosea Academy, along with Mai Kawakami, Reina Izumi, and Koito Minase, three girls who fight these creatures. High school life proceeds as normal until a certain incident reveals the truth of their world to them.