Mamotte Shugogetten!

In both stories, you have some kind of magical spirits/deities/goddesses hanging around the main protagonist. Both stories give off harem like vibes or cliches with the thought that there will be a love triangle. When in the end it ends up showing up as solely being a romance series with humorous supernatural shenanigans. Mamotte Shugogetten! does not follow as clear on its story I guess unless you plan to read the 11 volume manga series instead of watching the anime adaptation. Ah! My Goddess! is better in comparison to Mamotte Shugogetten!. So take Mamotte Shugogetten! as the bargain bin version of Ah! My Goddess! Mamotte Shugogetten! is a series that is underrated or obscure for good reasons. I will say that despite the great dislike people have for the Mamotte Shugogetten! anime I still have a fondness towards it because I know it's not the best series out there but it tries to still have fun with itself. Its fondness can be just as strong as one's fondness towards Ah! My Goddess! read more 

Both the female main character causes trouble for the male, but the difference is in Mamotte Shugogetten the girl lives in the house of a boy and in Fruits Basket the girl lives in a house with three boys because of some unexpected happenings. Fruits Basket is better, honestly.  

The main guy's father is always away from the house and always sends odd things to the main guy and the thing that the father send turns into a girl after the main guy opens it...Yup... exact same scenario. 

Both of these series have a male protagonist who awakens a mystical and mysterious girl. They end up having an adventure with them and there is also a romantic development between the male and female protagonist. The male characters are also very similar in their personalities