For anime similar to Heaven's Lost Property, there are a number of titles to choose from. The following list ranks the best anime out there that are like Heaven's Lost Property, with the order determined by votes from anime fans like you. The genres that best describe Heaven's Lost Property are action, fantasy, and harem, so many of these similar anime are in those genres.
Fans of Heaven's Lost Property may want to check out DearS, Chobits, or To Love-Ru, which follows a high schooler who one day, out of the blue, becomes the object of affection of an alien girl. Still there are other anime with similar elements to Heaven’s Lost Property like Sekireii, DBak and Test: Summon the Beasts, and Rosario + Vampire, which also centers on a boy who finds himself with a number of potential love interests; and as is the case with Heaven's Lost Property, the girl(s) are not human.
If you find that any anime that's similar to Heaven's Lost Property is not yet represented on the list, feel free to add it and help the list grow!