Sora no otoshimono. From wikipedia "The plot revolves around a boy in the town of Sorami named Tomoki Sakurai who is one day invited by his childhood friend Sohara Mitsuki and Eishirō Sugata (the leader of "The New World" club) to come at midnight to witness a strange object seen crossing through their town's sky. Tomoki goes alone and as the strange object comes close, Sugata calls to warn him to get away from it. What falls from the sky is a creature called an Angeloid named Ikaros.
Ikaros imprints on Tomoki after he rescues her from being destroyed by falling debris. She introduces herself as a "Pet-Class" Angeloid and offers to fulfill any wishes Tomoki may have. In time, she begins to pick up human characteristics from her involvement with Tomoki and more of her past is revealed. We soon discover that Ikaros has left "the Heavens" in disarray, and various Angeloids are sent to retrieve her."