Bands, Albums or Songs that got you into Death Metal And/or Black Metal.

1st death metal album: Amorphis - Tales From the Thousand Lakes
1st black metal album: Emperor - Anthems to the Welkin at Dusk
 
Metal: Sabbath or Scorpions or Ozzy (it was a long time ago)
Thrash: Metallica - Kill Em All
Death metal: Living Sacrifice or Mortification
Doom: Paramaecium
Black Metal: Horde

Yeah, those last three may seem weird, but it's where I was at the time :)
 
Godflesh is pretty much responsible for getting me into metal. Hymns was the first real metal album I had. But early on what caught me was Agalloch, Godflesh, Meshuggah, Candlemass, Dark Tranquillity, first 2 Opeth albums, Woods of Ypres and My Dying Bride. Not all of those bands are black and death, but oh well. Thank god i didn't catch that children of bodom plague.
 
I got into metal with Iron Maiden. I didn't get into death metal until I heard the song Slowly We Rot by Obituary. I have yet to fully embrace black metal.
 
Metal: Megadeth - Sweating Bullets
Death metal: Benediction - Grind Bastard
Black metal: Deströyer 666 - Unchain the Wolves

I don't know when I first heard that Benediction album, D666 was fairly recent though. I kept my distance from black metal for a lon time because, in my experience, so much of it is just noise.
 
Sorry, I have to put almost all the sub-genres...

Thrash Metal:

Metallica - Ride the Lightning

Death Metal:

Deicide - Serpents of the Light

Black Metal:

Nokturnal Mortum - Lunar Poetry

Heavy Metal:

Iron Maiden and Black Sabbath

Gothic Metal:

Trail of Tears - Profoundemonium

Progressive Metal:

Symphony X - The Odyssey

Power Metal:

Nightwish - Century Child

Doom Metal:

My Dying Bride - The Angel and The Dark River
 
I got interested in Death Metal via Ace Ventura when Cannibal Corpse played Hammer Smashed Face. Before then I thought death metal was just noise, but after seeing the film a few times I got interested and started borrowing death metal tapes from friends of mine and eventually someone copied Tomb of the Mutilated and Cause of Death and I was hooked.
As far as black metal I got into it via Cradle of Filth-Dusk... and her Embrace back in 97... From there I explored other bands.