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.
Stood in the Fire
One of my Ex's really enjoyed Full Metal Alchemist and Darker than Black.