Chobits is a nice slice of life show. College aged kid finds a humanoid robot in the trash and takes it home. Finds a way to wake it up and starts taking care of it.
Well I'm a woman and a couple of my favorite's are Elfen Lied, Angel Beats, and Neon Genesis Evangelion.
Ghost in the Shell, : Stand Alone Complex makes for an excellent gateway series for people who like CSI, etc.
One of my Ex's really enjoyed Full Metal Alchemist and Darker than Black.