There is an Angelic Layer Manga and Anime. However, because its been a while since I've read the manga and I just finished the anime, I'm only going to talk about the anime.
Title: Angelic Layer
Genre: Action, Comedy, Shojo-ish
Plot Summary: Suzuhara Misaki moves to Tokyo city in order to attend school and for a hope that she will see her mother, who left 7 years previous to work in Tokyo. After exiting the station, she sees on a big screen two people fighting. However, these are not people - rather they are Angels, which are dolls controlled by a Deus. These dolls are custom made, and they fight in Angelic Layer, which is the name of the sport. She is told all this by the scientist Icchan, who walked up to her and started telling her this stuff. Ignoring the possibibility that he might be a lolicon [AKA, pedophile][He isn't], she followed him into the Anglelic Layer store, where he went and showed her what to buy to create her own angel. After creating her own Angel, who she called Hikaru [which means Light], and making friends, Kotaro and Tamayo, she enters tournaments and goes on to become the Kiseki no Rookie [Miracle Rookie].
Analysis [Contains Spoilers][Highlight to View]: Its a decent enough anime. Its done by CLAMP, which makes some good anime/manga, but I do have some problems with it. Early on in the series, Kotaro developes a crush on Misaki, which is teased upon by Tamayo. However, later on in the series, Tamayo admits that she's had a crush on Kotaro for a long time. If thats the case, why did she even push him onto Misaki to start with? The other thing I can't get around is the fact that she is the Kiseki no Rookie. She starts playing, and then she never looses. She only lost once, and that was too Kotaro's little genius sister, Hatoko. She beat every opponent after that, continuously gaining in strength, without really appearing to. Additionally, the Champion, Shuko, who is her mom, lost to her. When she hadn't lost to 77 or so other players. Finally, there is the matter with her mom. Her mom, quite frankly, is a wuss. A gigantic one. She's afraid to see Misaki, because she's afraid of what Misaki will think of her. She doesn't want Misaki to see her in a wheelchair. However, by postponing it, isn't she just making it worse?
End of Spoilers
Analysis [No Spoilers]: Some of the fights are cool. I think that the plot is a bit iffy, but its a 26 episode show expanded from a 25 or so chapter manga. There really isn't much you can do with it. I think that the comedic moments are great, but sometimes it just pushes it. Some of the fights are good, some are bad. It seems like in order to make a new plot point in the fight, they introduce something, that they can miraculously explain away in all of the previous fights. While sometimes, it works, but other times ... I just can't buy it. Theres only so much you can ignore.
Additionally, when you 'launch' angels onto the layer, you say an opening shpeal. Which is kinda lame. And I really dont see how Hikaru can fall like the way that she does in that.
There isn't really much to the anime except for the tournament. The first 4 or so episodes deal with her starting, and then there is the tournament. The rest of the plot then deals with the tournament. The unimportant matches get an entire episode, and some of the 'big' matches, you never see the character again. If you do, its very very minor.
This is a cute anime, and ok for a laugh. Some of the fights are good, while others are meh. Watch it if you want.
First Image - Icchan talking to Misaki when she buys the Angel Egg.
Second Image - Athena, Angel to the Champion, launching her ultimate attack.
First Image - Hikaru on the Layer, with Misaki sitting in the controlling egg behind her.
Second Image - Hikaru kicking Mao, an opposing angel, during the same fight.
There are better images that I could get, but I have the episodes in .ogm format, which makes them hard to look through.