The Antlers

The Antlers are an alternative rock band based in Brooklyn, New York. In 2006, The Antlers began as the solo project of current front man, Peter Silberman. After releasing two full albums in this manner (Uprooted and In the Attic of the Universe), Silberman recruited Michael Lerner and Darby Cicci.

The Antlers are best known for their incredibly depressing Concept Album, Hospice, released in 2009.

Discography:

Uprooted (2006)
In the Attic of the Universe (2007)
Hospice (2009)
Burst Apart (2011)

The Antlers provides examples of the following tropes:

Album Title Drop: Burst Apart is dropped several times in "Rolled Together"
Anti-Love Song: "I Don't Want Love" is an obvious example.
Careful with That Axe
Concept Album: Hospice chronicles an abusive relationship, sung through the analogy of a relationship between a hospice worker and a dying patient. In the Attic of the Universe and Burst Apart also have shades of this, with their themes of helpless and dog metaphors respectively.
Drunken Song: "Every Night My Teeth Are Falling Out".
Epic Instrumental Opener: "Prologue" on Hospice.
Fading Into the Next Song
Grief Song: "Shiva".
I Am the Band: Silberman, for the first two albums.
Looped Lyrics: "Rolled Together" for the entire song.

Rolled together with a burning paper heart
Rolled together but not enough to burst apart
(repeat ad nauseum)

Love Nostalgia Song: Sort of subverted with "Kettering", which is about the singer wishing he hadn't fallen in love with someone in the first place.
Mondegreen: A minor example. "French Exit" contains the line "[...] you're gonna make this insincere" but, to many, the way it's sung makes it sound like "[...] you're gonna make this sin sincere".
Non-Appearing Title: "Kettering", "Atrophy", "French Exit", and "Corsicana", to name a few.
Ode to Sobriety: "Every Night My Teeth Are Falling Out" has the singer lamenting the fact that he keeps ending up sleeping with his ex against his better judgement while drunk and/or high.
Rock Me, Amadeus: The first few bars of "Bear" are are taken almost exactly from "Twelve Variation on 'Ah vous dirai-je, Maman'" by Mozart (aka, "Twinkle Twinkly Little Star").
Title-Only Chorus: "The Universe is Going to Catch You".