AI ga Tomaranai!, Aa! Megami-sama! Recommendations
Same type of story. Ah My Goddess is about a lonely guy meeting a goddess and they fall in love. A.I. Love You is about a lonely guy making an AI girl computer program that happens to come to life and they fall in love. Both are slice of life romances.
They are both about a guy suddenly having a girl live with him and they both deal with the romantic relationship between the two.
Both stories are about a young man who are unlucky with love. They've been rejected by the most popular girl in school and feel down about themselves. One day a miracle happened, or in these cases either a wrong number phone call (Aa! Megami-sama!) or a lightning storm (AI ga Tomaranai!?). They are granted with a too good to be human girlfriend. But what happens after is what makes this interesting.