It's hard for me to tell you becouse i prefere horror anime. xd
But i think Pandora Hearts, Soul Eater and Sword Art Online would be good.
Also White Album, Little Busters!, Walkure Romanze, Date a Live and Log Horizon.
Princess lover, Elfen lied, Another, Shingeki no kyojin [attack on titan], btoom, k-on, C-control, Da capo II, There are more but i forgot about most of them. all theese are my favourite.
EDIT; Death note, Highschool of the dead[must watch], Guilty Crown[must watch], Code Geass
Hacks, Highschool of the dead is bloody, But its amazing.
Elfen lied has a f*ckton of blood and gore in it but is also amazing, thats why I wanted you to watch them.
For now, I really would want you to watch Guilty crown, It's not bloody And it is just amazing. Look at concon's review of it, It's amazing, out of doubt the best anime for me.