Mahoromatic: Automatic Maiden

Vesper is a secret agency fighting an army of alien invaders by using super-powerful battle androids. Mahoro is Vesper's most powerful battle android and has won many battles, but she has little operating time left and soon will cease to function. However, if she lays down her arms and conserves her remaining power, the time she has left can be prolonged to just over a year. Mahoro is given an opportunity to live the remaining time she has as a normal human. She chooses to live as a maid for Suguru, a phenomenally messy high school student who lives by himself after his family passed away. (Source: Anime News Network)

Chobits

In the future, personal computers have developed into "Persocoms", mobile computers that look like human beings. Hideki Motosuwa, a prep school student, desperately wants to buy a Persocom but cannot afford to. One day he finds a Persocom that has been thrown away and decides to keep it. When he turns on the Persocom, all she can say is "Chii" so he decides to name her that. After a while it starts to become apparent that Chii is more than an average Persocom. Having much better performance, it seems that Chii might be a "Chobit", a type of advanced Persocom rumored to have independent thought. (Source: Anime News Network)