Dying Earth

The Earth is doomed, but it's going to take awhile to die so let's sit back and watch what happens. These stories tend to take place at the end of the Earth's life or at the end of time and are thus occur far into the future. It is a sub-genre filled with themes of world-weariness, fatality, reflection, lost innocence, idealism, entropy, exhaustion of resources, and hope. It's a very melancholy sub-genre— understandably so because the landscapes are often barren, sterile and the sun is often fading. This sub-genre may sound a bit like apocalyptic science fiction, but its difference lies in the cause of the Earth's death. The focus is not a cataclysmic event, but rather the end of time. As such this sub-genre has lots of overlap with fantasy in that it postulates fantastical versions of Earth's future.

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1 The Time Machine

By H.G. Wells. The root of the Dying Earth sub-genre.
2 Zothique

By Clark Ashton Smith. Stories that began to define the sub-genre and are the first to show readers a world vastly different, more fantastical, than our own.
3 Tales of the Dying Earth

By Jack Vance. A series, and the reason there is a Dying Earth sub-genre.
4 Dark is the Sun

By Philip José Farmer. Novel set 15 billion years in the future when the Earth's core is cooling. Framer does a noteworthy job building fantastical and weird settings.
5 Viriconium

By M. John Harrison. A defining series in the Dying Earth sub-genre because of its use of metafiction.
6 The Confluence Triology

By Paul J. McAuley. A trilogy that is noteworthy because it focuses on the end of a planet, but not Earth. This trilogy takes place on the planet humans inhabit after the death of Earth.
7 The City and the Stars

By Arthur C. Clarke A new take on the Dying Earth sub-genre because it focuses on the way people deal with technology that changes their worldview.
8 Till A' the Seas

By H.P. Lovecraft and R. Barlow . A story notable because it is about the last human alive on Earth, literally.
9 The Book of New Sun

By Gene Wolfe. These books are written as though a diary and so there is much left to the reader to decipher as the narrator journeys through long dead civilizations.
10 Hyperion

By Dan Simmons. So most of this series is in fact, not Dying Earth but it is a pinnacle of science fiction. The Poet's Tale: Hyperion Cantos in the first novel of Hyperion is a part of the Dying Earth sub-genre and it is the connection the readers have from Earth to the strange new universe of Hyperion.

Other Features of Dying Earth Science Fiction

Level of Real Science
Not so much. Science does play a part in Dying Earth stories, but think of it more as forgotten science and technology. Often science is more magical or fantastical than hard science.
Level of Grand Ideas/Social Implications
Massive. Dying Earth stories reflect on Earth and human history and extrapolate how things develop in the future. It is a sub-genre that makes one think because it takes place so far into the future there is lots of freedom for writers to explore lots of grand ideas.
Level of Characterization
General. Dying Earth stories are about a draw-out death of the planet and so while readers will encounter fascinating characters, the stories tend to be too drawn out over time to have deep complex characters.
Level of Plot Complexity
Big plots. Because of the whole end of Earth/end of time thing Dying, Earth stories cover lots of ground and the plots are necessarily large and often span huge spans of time.
Level of Violence
Variable. Violence is something that can happen when people are faced with the end of all things so it is bound to come up in these stories. However, Dying Earth stories tend to be more melancholy than violent.

Related Science Fiction subgenres

Apocalyptic is the obvious relation to Dying Earth and there are several overlaps, but the big difference is the cause of the end of all things because Apocalyptic Science Fiction focuses on a cataclysmic event.
Post Apocalyptic. Dying Earth may triggered be an Apocalyptic event and thus exist in a Post Apocalytpic world. However, Dying Earth is not so much focused on the actual "event" but more of the result of the "event"
Social Science Fiction makes its way into Dying Earth Science Fiction in its reflectivity. When a world comes to its end there is necessarily commentary on the societies that grew there.