My parents were always supportive if I wanted to hear new music... but considering I was born in the 80's (gag me for most pop 80's stuff), and grew up in the Southwest in the 90's (Again, bleh for 90's pop), I really did inherit most of my early taste from them. Classic Rock galore, and not just light stuff either, My parents liked the Beatles, Rush, Queen, and other such classic softies (Barring Bohemian Rhapsody that is), but my dad, bless him, liked Judas Priest, Led Zeppelin, Ozzy, ZZ Top, Motley Crue, and even introduced me to Metallica!
From there I developed a taste for Industrial (NIN, Rob Zombie) and other classic Heavy groups (Anthrax, Iron Maiden, Megadeath) but also for Techno, DDR in particular, and later on Power Metal (Alestorm, Dragonforce, Rhapsody of Fire etc)
But thankfully, my parents are still pretty cool in their musical tastes, my dad digs on NIN with me sometimes, and we both like Them Crooked Vultures, and my mom is slowly opening up to Symphonic Metal. Go them!
EDIT: My mom also digs on Skillet, which I find kinda funny.