Nineteen-year-old ronin Hideki Motosuwa desires two things more than anything else: a girlfriend, and an expensive humanoid computer (known as a 'persocom'). But with his dead-end job and no financial aid from his parents, owning a persocom seems impossible... until he finds a blond-haired female persocom tied up amongst a pile of trash! After getting her home and figuring out how to activate her, even the computer-illiterate Hideki realizes there is something unusual when it appears she can only say one word - Chii. Is she just broken, or is there more to this persocom than her behavior lets on?
If you took a liking to Claire from Fairial Garden, you could probably give Chobits a try. While it's nowhere as cute as Fairial Garden (and it even contains some ecchi), it does feature a similar character to Claire (namely Chii). Like Claire she is super innocent and her love towards the male lead is of the unconditional type.
A year after their spaceship crash-landed on Earth, the alien species known as 'DearS' have been accepted into the Japanese citizenry. They are adored by many fan groups and trusted by most humans - with the exception of Takeya Ikuhara. Kind-hearted but resistant to change and skeptical of the DearS' seemingly-friendly behavior, Takeya tries to have as little to do with them as possible. But after he saves a girl from an incoming truck, and she turns out to be a DearS, Takeya ends up being far more involved with them than he could have ever imagined.
So, in this alternative reality some sort of non-human being (the Dears in case of DearS and Fairia in case of Fairial Garden) is all the rage among the population. Everyone, but our male lead, wants to have one of those. Yet, it is him who comes into possession of a special one (much to his dismay). From there, despite his initial negative attitude, he gradually starts to care about the one in his care. Note that Fairial Garden is awfully cute and unlike DearS it's ecchi free. If the first part of this recommendation got you interested and the second part didn't discourage you, you might as well give those two manga a go.