Angelic Layer was one of the anime I watched growing up.
I was recently reminded of it by the anime Gundam Build Fighters which also has a similar premise, so I thought, "What the hell, let's rewatch Angelic Layer. I've forgotten much of the details anyway."
I enjoyed the series. The battles were fun to watch and definitely enjoyable. The rivals all have some kind of special ability which makes every fight unique. However the damage is not consistent, sometimes a punch or kick takes out half the life bar, and other times it does barely a scratch (sometimes I think they should have gotten rid of the lifebar instead....). Also I didn't get how the tournament works.
Story is good enough, nothing special. Misaki, our protagonist who has a disappeared mom, moves to tokyo. There she meets new friends, discovers the sport Angelic Layer and becomes a player (or Deus, as the anime calls the players) of the sport. The characters were interesting and Icchan is one of my favorite characters. He's one of the comic relief-there are funny moments here and there which made me laugh.
Overall I'd say it's a good anime. If you like good one-on-one battles (or maybe you enjoyed Build Fighters and is looking for something similar while they're making the second season) then I'd recommend this anime to you.