 If you liked
Aa! Megami-sama!
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 ...then you might like
Video Girl Ai
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Two OVAs from the early 1990s where the main plot device is a suddenly appearing non-human, but human looking, girl. Obviously, the surprised male lead falls in love with her. And by the end of the short (5/6 episodes) series, the mood shifts from comedy to drama. The series even straight lift specific elements from each other (looking at you, girl crawling out of a TV).
In terms of differences, Video Girl AI is more slapstick-based and has a more involved plot. Aa! Megami-sama has the better production quality.