If you ask a knowledgeable role player to list the genres and settings that have been used for published games, the list is likely to include fantasy, horror, super heroes, and "science fiction". However, this answer is misleading, because "science fiction" (or SF) is a label covering a huge range of options. (Actually, so are the others, but SF covers the most.) Because the "flavour" of SF can vary so widely, published games generally go for one sub-category. Those taken include star hopping "space opera" (Traveller, Star Wars, GURPS: Space, and many others), cyberpunk (Shadowrun, Cyberpunk, et cetera, et cetera), various flavours of "post holocaust" (Twilight 2000, the wonderful GURPS Reign of Steel, and small sellers such as The Morrow Project), and oddities such as Paranoia. (Warhammer 40,000 is a "gothic", eccentric exercise in space opera. It's also a wargame, not an RPG, of course.) However, there is one category that has received very little treatment and deserves more.
"Far future" SF is more than just SF set thousands of years from now. Remoteness is part of the flavour, but some stories set aeons ahead "feel" less remote than others with dates only centuries hence. Games where armoured space marines (good or bad) fly from star to star, blasting bug eyed monsters (or people), are basic model space opera, whatever their "future history" may be. This article is about a brew with flavours of space opera, but much more rich and strange.
It may be easiest to define the subject by reference to a few examples. A classic chronicler of the strange far future was the late Cordwainer Smith. In relatively few stories, and only one actual novel, he created the weird future history of "The Instrumentality of Mankind". In it, humanity spreads to the stars, using a variety of starship designs, all with odd features. Earth, and to varying extents other planets, are ruled, guided, and guarded by the "Instrumentality" itself, a government above governments whose leaders are generally brilliant, honourable, ruthless, and a little twisted. Future society is served by "underpeople", animals modified to human like form and intelligence, but kept as, effectively, slaves. The stories cover various aspects of this society, including battles with space dwelling monsters (The Game of Rat and Dragon), space wars won by bizarre super weapons (Golden the Ship Was Oh! Oh! Oh! and Mother Hitton's Littul Kittons), the deadly threats that space travel might encounter (The Crime and the Glory of Commander Suzdal and Under Old Earth), horrific prison planets (A Planet Named Shayol), and the peaceful revolution of the underpeople (The Dead Lady of Clown Town and The Ballad of Lost C'Mell). Stories in which the young Casher O'Neill wanders space are collected in Quest of the Three Worlds; all the others are nowadays to be found in The Best of Cordwainer Smith and The Instrumentality of Mankind. Much comes together in the novel Norstrilia, in which a teenage hero buys the planet Earth and helps the underpeople.
These may sound like very conventional space opera, but the point is Smith's very personal style. His future Earth is dominated by a tower twenty-five kilometres tall, built as a spaceship but never flown; far beneath it, the servant underpeople make a society of their own. The Instrumentality has invented subtle ways of governing, but it can be defeated by the right combination of honesty, deviousness, judgement, and luck; it uses all of these things, and more, so that a bizarre universe can never threaten Earth quite as it thinks. These stories are both wonderful reading and a major part of the history of SF.
A more recent writer who has looked to the far future is Gene Wolfe, with his well known "New Sun" cycle; The Shadow of the Torturer, The Claw of the Conciliator, The Sword of the Lictor, The Citadel of the Autarch, and The Urth of the New Sun. These are set in a world in decay, both physical and spiritual, where much is half forgotten; the resulting "feel" sometimes verges on fantasy rather than SF, with swords commonplace and more powerful weapons used but barely understood; the plot's metaphysical elements add to this effect. However, the visiting aliens, and the black holes, and the moon blurred because it now has an atmosphere, make these unambiguously futuristic SF.
Another relevant novel is Nightwings, by Bob Silverberg. This is set in an era where humanity, having dominated the galaxy for a while, has over-reached its abilities, resulting in a damaged Earth where much great technology has been lost, and society is organised and stabilised by a system of guilds, some of them specifically for genetically modified humans. In the book, Earth is easily conquered by a fairly benign alien race with an ancient grudge against humanity, but may be "redeemed" by new philosophies. Silverberg has also produced other stories with remote, baroque settings; he seems more comfortable with such topics than most writers.
David Zindell is influenced by Wolfe, at least in the writing style of his Neverness and its sequels, but is still a fine writer in its own right. Neverness tells the story of the rise of a brilliant but rather annoying young pilot in a future guild of pilots - a closed shop of intuitive mathematicians who effectively control galactic travel. The guild is based on a long settled ice world, in a strange and beautiful city, and the plot spins out from there to take in intelligences the size of star clusters, human races who have adapted themselves to live on water worlds, immortality, higher maths, and the fate of the universe. It also has deadly rivalries, space battles, and some great characters, and is a "must read" for those looking into this field.
Finally, this list would be incomplete without a mention for Olaf Stapledon, a '30's writer who took a cosmic viewpoint to illustrate his complex philosophical ideas. His books are heavy going, and probably work on too large (and philosophical) a scale for the purposes discussed in this article, but they are central to the "far future" sub genre. Last and First Men, his first and most famous novel, covers 2,000 million years and eighteen species of humanity; Star Maker covers vast tracts of space and multiple alien races.
Among other books to look for are A World Out Of Time, by Larry Niven; The Time Machine, by H.G.Wells; Against the Fall of Night, or its re written version, The City and the Stars, and others by Arthur C. Clarke; Sunfall, by C.J.Cherryh; and various recent books by Greg Bear.
The main common feature of these stories is that they take a LONG view. Between today and their "now", a lot happens good, bad, and most important of all, different. Men may well go to the stars, may even found galactic empires empires that fall as well as rise. New technologies, new sciences, may arise and sometimes, they may be forgotten. Whole new intelligent species might be encountered or created; the moon might be given an atmosphere, even the solar system might be rebuilt - and all of this is part of history for the inhabitants of the age, the mechanisms perhaps lost, the consequences part of everyday life. So the first thing that strikes the reader is atmosphere; what is described is worlds with few direct connections to our own, and things are different there. Because the vast sweep of history behind the setting has had down swings as well as glories, the stories are often rather melancholy in flavour, although catastrophe and devastation are not the name of the game; think of run-down civilizations, still with a lot of grandeur, rather than worlds in flames. (Of course, the future histories involved are so long that there can have been some world-shattering disasters as well as glorious high points, but they aren't the point of the exercise.)
This style of decay has one common aspect; science and technology have often slipped back as part of the process. This means that there may be machines "lying around" which characters can use, but never properly understand; similarly, "ancient" genetic tinkering may have produced species and variations of species that the reader doesn't recognise. All of this is worked into the fabric of the setting; the characters take many things we would find strange entirely for granted, even if they don't understand them. Intelligent beings in "Far Future" stories can include humans and extraterrestrial aliens, but also "variants", many of them products of that "half forgotten" genetic engineering. Indeed, utterly bizarre "aliens" can even turn out to be of human descent, albeit heavily adapted for strange new worlds. The "real" aliens may, in fact, be too weird for humans to comprehend (after all, they "have" to look strange in a very strange world!); modified humans and terrestrial animals can provide more comprehensible weirdness. Attitudes to this can vary; in Neverness, genetic tinkering has come to be regarded as an obscenity, while Smith's underpeople are slaves, and Stapledon's human race simply evolves over vast time scales; certainly, some kind of limitations on tinkering prevent characters in these stories being too incomprehensible to us. Often, relatively "pure" humans view other forms of intelligence as inferior; this lets the writers show noble struggles among the oppressed, seeking to make humans recognise their moral rights.This, however, suggests that some things don't change else the stories would be boring for readers. Because so much is changed and different, writers can use the Far Future to show what they think is genuinely constant and consistent. Human nature heroism, greed, honesty, ambition, pettiness, nobility all this recurs in such stories, albeit sometimes in strange new shapes. The Far Future is a remarkable place to visit.
Roleplaying campaigns set in Far Future worlds are rare, but should be possible. The difficulties would include the sheer complexity of the setting, the scale of things, and the many odd features that would have to be included; although I personally don't always like the use of standard "published worlds" in games, it might be easier, at least to start with, for most GMs to use a "known" setting, such as Wolfe's Urth, the Instrumentality, or Neverness, and players should be encouraged to read the source material.
Rather than try to work PCs into the events of the books, it will be best to find "gaps" into which scenarios can be plugged; the Far Future is a big place, with plenty of uncharted corners. This isn't to prevent anyone using characters from the books as NPCs; I myself have run a scenario where PCs were employed by Lord Jestocost, and assisted by C'Mell, a couple of years after the events of Norstrilia (to tie up some loose ends from that book). However, use of "book" characters as PCs is probably a bad idea; they tend to have very specific stories and objectives, and are often radically changed during the published tales. Anyway, readers often have strong ideas about these characters, and may be irritated by the ways other players handle them.
The advanced technology of these settings may introduce some problems. To begin with, weaponry may be rare or commonplace, but it is usually advanced enough to be very deadly, which in turn makes fight scenes the staple of so many games a Bad Idea. Well armed PCs may have short and glorious careers of psycopathic behaviour, but sooner or later, the authorities who are usually very smart and very powerful, will catch up with them, and that could be terminal, for the characters' freedom if not their lives. There's a case for seeing all this as a good thing violence shouldn't be the be-all and end-all of games, but some players may disagree. If you are confronted with a bunch of Hack & Slash junkies, play a different game.
That's a matter of taste; what makes work for the GM is the high level of transport technology. In a fantasy game, it's relatively easy to keep lower-level PCs to one small-ish area; Far Future characters, with starships and air cars, can find it far easier to blunder into areas the GM hasn't mapped yet. The answer to this is for the GM to build a good general idea of how the game world works, then to improvise like crazy in emergencies. However, this is tricky, and some very good GMs can't always handle it. If in doubt, use a setting from a novel, throw a lot of clear plot hooks at PCs that keep them in places you know, and practice bluffing hard.
"Half-forgotten" technology ("old tech"), and very advanced science generally, is certainly a part of Far Future settings. Knowing this, and remembering Clarke's Law ("Any sufficiently advanced technology is indistinguishable from magic"), the GM of a Far Future game may tend to use high tech gadgets the way that D&D games use "magic items". That's not entirely silly; the two effects are not dissimilar, (Look at Smith's Alpha Ralpha Boulevard, or the weapons in Wolfe's books), but there are differences; if players come to believe that this is just a fantasy game with starships, why not play a fantasy game? If the campaign setting has technology at its peak, most of its products should be "routine"; even "special" gadgets should be interesting, but not usually awe-inspiring for the PCs; if something can be done once on "current" knowledge, it can be done twice. If knowledge has fallen significantly, then the GM has a bit more freedom to produce "one-off" super-machines, but they should usually be consistent with at least a vague idea of the pattern of the old tech, and ideally, players should come to believe that they are comprehensible, if not currently comprehended. (Smith's "Abba dingo" is an exception to prove the rule something so special that it cannot be repeated, so far outside human ideas of free will that it offends the spirit of those who encounter it.)
Given a setting, scenarios are another question. Chasing treasure feels less satisfying in a world where many people live in luxury undreamed-of in the twentieth century, and mercenary service is a dubious prospect in the face of such potent weapons. Two valid possibilities are The Quest and The Revolution - both long term campaign objectives that can lead to all sorts of subsidiary adventures. If you, as GM, decide on such a framework, then do make sure that the PCs have the right skills and personalities. If they are going to help the underpeople during the Rediscovery of Mankind, then they should mostly be animal-derived underpeople, perhaps with some sympathetic off worlders or suchlike for variety (ordinary Earth humans probably being too well controlled, Lords of the Instrumentality being far too powerful and tied up with their duties). If they are going to wander through a loose interstellar quest in the galaxy of Neverness, then they will probably need at least one pilot, and the other characters will need to be able to get on with pilots.
The rule system to use is, as ever, a matter of taste. The best bets might be either to adapt a good set of space opera rules (such as Traveller - add some skills, change some career paths), or use some specifically "generic" set such as the Hero System or GURPS. "Points design" systems may well be the best way of ensuring fair and balanced PC groups in settings where potential character types are quite as diverse as this. In any event, the GM will have to decide what skills, abilities, and background features are appropriate for the setting, and which are banned or unlikely; the special features for non humans will also need deciding. If you are using a large range of "adapted" species, then a very flexible system may be necessary; look hard at the Hero package deal rules, or the material in GURPS Uplift. A set of weapons stats may also be necessary, if only to scare players with the gross damage levels and dissuade them from combat. Some Far Future stories feature "psionic" powers, such as telepathy; if they appear in the setting you are using, pay attention to the rules for them in your chosen system. Then be ready for (and hopeful of) some very strange character concepts from your better players!
So this is the Far Future. It's probably the most complex, tricky, fascinating, breath taking area left to role playing. I wish plenty of good luck to anyone brave, and smart, enough to head that way.