Kidou Tenshi Angelic Layer, Chobits Recommendations
The plots of both these anime originate from the same manga-ka, and deal with the relationships that can develope between humans and machines. They are both very sweet and very emotional with a little bit of humour thrown in. Chobits is a bit more mature, however, and has a darker tone to the plot at times.
Angelic layer is based on same universe, but on previous age where the technology behind chobits were developing. It is separate story, only the sidelines of the story bring this up.
The technology used by these dolls later on developped as body structure for chobit units.