Metallica's three from that period (Master, Justice, Black).
Iron Maiden's "Seventh Son", "Somewhere in Time" and "Fear of the Dark".
Slayer's "Reign in Blood", "South of Heaven" and "Seasons in the Abyss".
Kreator's "Pleasure to Kill", "Terrible Certainty", "Extreme Aggression" and "Coma of Souls".
Guns 'n Roses' (I consider them metal) "Appetite for Destruction", "Use Your Illusion I" and "II".
Bathory's "Hammerheart" and "Blood on Ice" are pretty essential, at least in my book. As is his four black metal albums. More so, actually, than his viking releases.
Death released some classics: "Human", "Spiritual Healing", and "Symbolic".
There are also a lot of norwegian black metal albums from that period that I consider extremely essential:
Burzum - "Aske", "Burzum", "Det Som Engang Var", "Hvis Lyset Tar Oss" and "Filosofem".
Darkthrone - "A Blaze in the Northern Sky" (partly death metal, I know), "Under a Funeral Moon", "Transilvanian Hunger" and "Panzerfaust".
Emperor - "In the Nightside Eclipse".
Gorgoroth - "Pentagram" and "Antichrist".
Immortal - "Diabolical Fullmoon Mysticism", "Pure Holocaust" and "Battles in the North".
Other than that:
Blind Guardian - "Imaginations From the Other Side"
Fullmoon - "United Aryan Evil" (It'll be re-released soon)
Graveland - "Thousand Swords"
Katatonia - "Brave Murder Day"
Nokturnal Mortum - "Goat Horns"
Summoning - "Dol Guldur"
The Gothenberg scene:
At the Gates - "The Red in the Sky is Ours", "With Fear I Kiss the Burning Darkness" and "Terminal Spirit Disease".
Dark Tranquillity - "Of Chaos and Eternal Night" and "The Gallery".
In Flames - "Lunar Strain" and "Subterrenean".
I only chose well known releases, as those are the ones easiest to obtain. Maybe I'll add some "cult" releases later.
