For brevity (and my storage limits) I've narrowed this down to my physical collection. Every album listed here is one I currently own on CD, cassette, or vinyl.
I have a growing collection of digital albums made up of far more eclectic and eccentric picks than what I could thrift in person. I'm still deciding how I want to factor these in.

Mer de Noms
A Perfect Circle

The Art of Drowning
AFI

Jagged Little Pill
Alanis Morrisette

Facelift
Alice in Chains

Dirt
Alice in Chains

Jar of Flies
Alice in Chains

Judgement
Anathema

A Fine Day to Exit
Anathema

A Natural Disaster
Anathema

Relationship of Command
At the Drive-in

Starve
Blood Youth

Surrender
The Chemical Brothers

Musick to Play in the Dark2
Coil

B-Sides & Rarities
Deftones

The Singles 81—85
Depeche Mode

The Singles 86—98
Depeche Mode

Delta Machine
Depeche Mode

Worst Case Scenario
dEUS

Lost Souls
Doves

Version 2.0
Garbage

This is Where the Fight Begins
The Ghost of a Thousand

Demon Days
Gorillaz

Greatest Hits
Guns N' Roses

High Times: Singles 1992—2006
Jamiroquai

Sound Awake
Karnivool

The Great Cold Distance
Katatonia

The Fall of Hearts
Katatonia

Blessed by the Burn
Left Behind

Meteora
Linkin Park

Blue Lines
Massive Attack

Protection
Massive Attack

Play
Moby

Origin of Symmetry
Muse

Three Cheers for Sweet Revenge
My Chemical Romance

The Black Parade
My Chemical Romance

May Death Never Stop You
My Chemical Romance

Incesticide
Nirvana

Nirvana
Nirvana

Ignition
The Offspring

Blackwater Park
Opeth

Death to the Pixies
Pixies

Black Market Music
Placebo

Vanishing Point
Primal Scream

Invaders Must Die
The Prodigy

Come Clean
Puddle of Mudd

Different Class
Pulp

Automatic for the People
R.E.M.

Monster
R.E.M.

E-Bow the Letter
R.E.M.

Pablo Honey
Radiohead

OK Computer
Radiohead

Rage Against the Machine
Rage Against the Machine

By the Way
Red Hot Chili Peppers

()
Sigur Rós

Takk...
Sigur Rós

Greatest Hits: Rotten Apples
The Smashing Pumpkins

Irresistible Bliss
Soul Coughing

Xen Cuts
Various Artists