It's not anime music, they're just songs from regular japanese bands. The songs a were never utterly dedicated to the anime series, in the first place. Your assumption's pretty weird, if you'd ask me.

But anyway, let's get on-topic:

Opening Theme 1 - .Hack//Sign
Opening Theme 2 - Rurouni Kenshin
Opening Theme (1) - Hellsing
Opening Theme 7 - BLEACH
Ending Theme - Gundam Zeta
Ending/Opening Theme - Berserk
Opening Theme 2 - One Piece
Opening/Ending Theme - Neon Genesis Evangelion
Opening Theme - Rosaria To Vampire
Ending Theme - Rozen Maiden ~Traümend~
Ending Theme 3 - BLEACH
Opening Theme - Persona: Trinity Soul
Opening Theme - Gunslinger Girl: Il Teatreano
Ending Theme - Vampire D Hunter
Ending Theme - Bakuretsu Tenshi

There, just to name a few.