Absolute Boyfriend (aka Zettai Kareshi) is a manga series by Yuu Watase, the creator of Fushigi Yuugi and Ayashi no Ceres. This story focuses on a girl who accidentally orders a robot that is the "perfect boyfriend." Of course, there's a twist as the robot actually develop real feelings of love for the girl. Not only does the robot love the girl but she also has a childhood friend that has feelings for her as well.
Yep, this is pure shoujo fantasy but it's one popular enough to garner a live-action drama adaptation in Japan and another live-action version to premiere in Taiwan. If you're interested in checking out the manga, it's available in America from Viz.
Image Archive (.zip)