I have too many. I like metal, and weird/interesting music. I have apprication for everything, ragging on someones style of music is gay.
Protest the hero, Alexisonfire, Killswitch Engaged, Underoath, Atreyu, Avenged Sevenfold, Red Hot chilli Peppers, The Mars Volta, Metallica, Death From about 1979, Led Zepplin.
But to keep it to 3 or less is ridiculous, there's just way too many bands that are too good to not mention. I'd have to give you 3 bands per genre, then maybe I'd be able to scratch the surface.
There are too much. But right now I'm a lot into metal so just to name a few: Amon Amarth, 3 Inches of Blood, Opeth, Zao, In Flames, The Haunted, As I lay Dying and so many I forget...