I have started to get more interested in series that contains one or more characters that are A.I. - Artificial Intelligence, aka robots that looks and acts like humans.

I will list the ones I have seen or read,, and I will use the spoiler tag for some.

Uta no Prince-sama


Chobits
Well, Chi, obviously. She's the main character and are found by Hideki.

DRAMAtical Murder


DearS
(I know these are more like aliens, but they are sort of A.I.)
Exactly one year prior to the beginning of DearS, humanity made unprecedented contact with extraterrestrial life. Forced to crash land into Tokyo Bay when, en route to their home planet of Thanatos, their spacecraft breaks down, 150 humanoid aliens are naturalized into Japanese society and affectionately nicknamed "DearS"; a portmanteau of the words "Dear" and "Friends".

Takeya Ikuhara is a temperamental seventeen-year-old Japanese student attending the fictitious Koharu High School with a strong prejudice against the DearS. Due to a childhood scare, he believes that the aliens are fake, worthless beings that have generated nationwide overhype and are secretly plotting to take control of Earth.

On his way home from school he discovers a homeless DearS who, after fainting and much to his annoyance, he feeds and shelters in his apartment. The girl, who he nicknames Ren, is infantile and friendly, and grows obsequious and dependent upon Takeya, a responsibility he tries to disassociate himself from. Her oblivious tenacity keeps her around, however, and over time, realizing Ren's genuine care and empathy for him, Takeya has a change of heart. Unfortunately, because Ren is deemed defective, DearS headquarters orders her arrested.

Absolute Boyfriend
A real romantic and tragic love story.
Riiko Izawa has never had a boyfriend and she has been rejected by every boy she has ever had a crush on. When she returns a lost cell phone to an oddly dressed salesman, she mentions wanting a boyfriend. To thank her, he directs her to his company's website, Kronos Heaven. When she visits the site, Riiko finds it's a site to create your perfect lover. Thinking it's a game, she customizes and accidentally orders one. The next day, her new lover arrives. Following the instruction manual, she kisses him to wake him up which configures him to be in love with only her. She names him "Night." Three days later, she is shocked to learn that she only had him for a free trial for 72 hours. The salesman, Gaku Namikiri, tells her that she must now pay ¥100,000,000 for Night, however, they will waive the fee if she helps them to collect data about how women think and feel to help perfect future models.
Riiko must now keep Night's true nature a secret from everyone around her.

Hybrid Child
A more yaoi series, but brilliant. One manga volume and four OVA-episodes exists.