Death Metal = mostly simple heavy riffing, dark/deep grunted vocals, lots of drums (blastbeats anyone?), themes about killing/death/Satan. ex: Cannibal Corpse, Deicide, Obituary, Death.
Black Metal = the guitar tone is either all out riffage or very light, the vocals are shrieked/hissed and are about Satan/occult/evil, blastbeats galore or very little drumming to take an atmospheric effect. ex: Mercyful Fate, Bathory, Burzum, Mayhem.
Thrash Metal = <33333333333. RIFFAGE DOWN YER FUCKIN' THROAT, very aggressive drumming (snare drum + clash + bass drum) with shouted vocals. Not screamed or grunted, shouted. Think punk just trying to be less punk. ex: Slayer (pre-Seasons in the Abyss), early Metallica (pre-Ride the Lightning), Exodus, Death Angel, Coroner, Dark Angel, Testament, Torture Squad, Sepultura (pre-Arise), Annihilator, Forbidden, Nuclear Assault.
Speed Metal = very riffy. A lot like thrash, but not as aggressive in vocal department or drums. ex: Judas Priest (Unleashed in the East = speed fucking metal), Iron Maiden.
Hair Metal = balls to the fucking wall heavy fucking metal revolving around womanizing. When people say heavy metal, this is often who you think of. ex's include Motley Crue, Twisted Sister, W.A.S.P., etc.
Power Metal = lots of melodic riffs, drums vary, the vocals include stuff about fairy tales or stories and are often the cleanest you'll find in any metal. ex: Iced Earth, Helloween, Blind Guardian, DragonForce.
Melodic* = very melodic and progressive compared to the original genre. i.e. Melodic Death Metal = more progressive and varied in the guitar riffs, and the vocals aren't all grunted. They could be screamed! ex: The Black Dahlia Murder, Arch Enemy, Hypocrisy.
Metalcore = crap. Heh. I can't give you a good definition. Think hardcore trying to be metal, but failing miserably. Apparently good live though. ex: Unearth, Killswitch Engage.
Grindcore = punk meets thrash and has an ugly love child. Characterized by extremely fast (240 bpm easily) drumming, incomprehendable riffing and lyrics, and very short songs (often lacking a song structure). ex: Terrorizer, Napalm Death, Carcass, Pig Destroyer.
I'll elaborate later. Food is waiting!