Here are a few of the books, movies, and other sources that inspired Sufficiently Advanced. If there are sources that inspired you in your own games, feel free to add them here!
Singularity Sky by Charles Stross. A great example of what happens when a pre-singularity culture attacks a post-singularity one. Entangled data transmission, black-hole driven starships, and plenty of nanotech behind the scenes. Also, one can make a good compare & contrast exercise between the Eschaton and the Transcendentals. Its sequel, Iron Sunrise, works almost as well.
The Golden Age by John C. Wright, and its sequels (The Phoenix Exultant and The Golden Transcendence). You want humanity in a thousand variations? Technology so extreme it creates entire new societies just by its very existence? Giant piles of drama? Right here.
The movie GATTACA could fit nicely into the timeline of SA, roughly 10-20 years before the nanotech wars (and thus thousands of years before the game’s default start date).
The Collapsium by Wil McCarthy, and its sequels (The Wellstone, Lost in Transmission, and To Squeeze the Moon). This is the primary source for the Replicants, programmable matter, and the arbitrary frequency doubler (which makes most Stringtech possible). In fact, everyone in this series is basically a Replicant.
Dune by Frank Hebert is a great example of humanity enhanced without the aid of computers. If you’re wondering what high Metatech and Cognitech can do, take a look in here.
Hyperion by Dan Simmons, and its sequels (Fall of Hyperion, Endymion, and Rise of Endymion). The AIs here and the Transcendentals make for another good compare/contrast exercise. The web of worlds was too good an idea not to borrow, and the Ousters are completely awe-inspiring. If you haven’t read the series, I won’t spoil it for you except to say that the second and fourth books utterly overthrow everything you read in the first and third. Highly recommended.
Bloom by Wil McCarthy and The Diamond Age by Neil Stephenson are both excellent examples of what one might do with nanotech. If you’ve read Diamond Age, the nanotech in SA is much closer to Seeds than to the Feed. Diamond Age’s franchised nations are also a very catchy idea.
Engines of Creation by K. Eric Drexler is a must-read for anyone involving nanotechnology in their works, though Drexler himself has said that some of its predictions (especially grey goo) are a bit extreme.
Foundation and its myriad sequels, by Asimov and others, and Psychohistorical Crisis by Donald Kingsbury. These are the only books I’ve seen that tackle the idea of highly advanced social science. Crisis’ “fam” technology is a good analogue to the netural meshes in this game.
It has been pointed out to me that many episodes of the original Star Trek series make for surprisingly good S.A. plots, especially those dealing with first contact, skirting the Prime Directive, or technology gone bad.
Vernor Vinge’s A Fire Upon the Deep influenced not only the group-mind society, but the Aia as well. Good primary source for these two odd groups, and an excellent book as well. It and its companion, A Deepness In The Sky, are excellent references for comprehensible non-human activity as well.
Greg Egan’s Diaspora is an example of what this game’s Stored might some day become, and where the cultures of Sufficiently Advanced might one day go. The humans still living on Earth are also a great example of how a Heterolinguist civilization might hold together, though they weren’t the original inspiration for that society.
Hannu Rajaniemi's Jean le Flambeur trilogy about a semi-reformed thief in a trans- and post-human Solar System where the Sobernost group minds strive to accomplish their great work, Oortians live in the vast outer system, Jupiter is gone, gamers play with quantum entanglement, Mars is … Mars is odd. The Quantum Thief, The Fractal Prince and The Causal Angel.
If the Union were a group-mind and ran Mars, it would look like the webcomic A Miracle of Science
Orion's Arm is a multi-authored online science fiction world-building project, first established in 2000 by M. Alan Kazlev, Donna Malcolm Hirsekorn, Bernd Helfert and Anders Sandberg and further co-authored by many people since. The website itself is a fun browse and inspiration for civilizations, societies and technologies. There are also 2 books Against A Diamond Sky and After Tranquility. This was also the inspiration for the Orion's Arm parts of the forum.
Big Ideas, Grand Vision is a roleplaying science fiction setting written by Anders Sandberg 1999. It is intended as hard science fiction, dealing with the question "What can humanity become?" It was originally run using the Alternity system, but should work fine in most other general systems.