Saber Marionette J

Earth begins to experience overpopulation problems in the future (well, we have that problem now actually, but it's much worse then), so ships are sent into space to colonize other planets. One ship, the Mesopotamia, has some rather serious technical difficulties and only one escape pod conveying six males is jettisoned to the planet Terra II before the Mesopotamia explodes.
This poses a dilemma. Either the six survivors could wait out their lives alone, or they could make the best of their situation and clone themselves to build a population for this barren planet.
The latter is the decision that is made, and three centuries later countries have formed, filled with men. The more wealthy of the citizens have androids called "marionettes" do their work for them. Marionettes are made to look like the human females, and are quite limited for the most part in their abilities and interactions with humans.
Saber Marionette J begins with the story of a poor boy named Otaru Mamiya and his encounter with a marionette named Lime who is unlike any other he has ever seen. She behaves and expresses herself no differently from a human.

This is a great series and I cannot recommend it enough.