Both Angelic Layer and .hack//Legend of the Twilight Bracelet share in the fact that they are both happy and light reads. They both take place in an advanced semi-future with cyber games, although the world of .hack and 'The World' can seem darker at times.
A strong will and an egg. Both series pair these two elements together with a bit of childhood innocence. In both stories, the main character has a strong desire and faith in what comes from the egg. While Angelic Layer may be a tad old, it's worth the look if you like the feel Shugo Chara! has in it, as Angelic Layer has a similar one.
Chobits pretty much takes place in the same universe as Angelic Layer, making it somewhat of a spin-off. If you pay attention, you'll see light references to Angelic Layer. It's even mentioned once later in the manga. The creator of the Angelic Layer game is also the creator of the Chobits persocoms. However, the connection between the anime adaptations is very different.
Magic Knight Rayearth and Angelic Layer are not that similar in terms of storyline, but if you want to check who inspired Suzuhara Misaki and her angel Hikaru, reading the first series of Rayearth is a good call.
Shidou Hikaru has the same determination and fighting spirit of Misaki/Hikaru. Read both series and compare the development of these two "little" girls with a lot of challenges to win in their lives.
Instead of life size dolls, Angelic Layer has small "Barbie-sized" dolls (aka Angels) that are pitted against each other by their owners (aka Deuses), who control the Angels with their minds. The main character Misaki ends up buying one on impulse when she first arrives to move in with her aunt and ends up getting involved in an Angelic Layer tournament.