An Arthur C. Clarke world:
Using nuclear-propulsion spaceships, people have been busily exploring the solar system since the early 70s.
People have been on Mars since the mid-80's, and there are now bases on the Moon and Mars, and a teeny one on rather inhospitable Venus. Mars is dry and dusty and cold, and has air too thin to suit humans, although there is some tough vegetation and some extremely specialized animals, along with some odd wind-drifting half-plant, half-animal things that multiply rapidly in warm weather and vanish entirely during the cold. Due to the logistics, the bases are still quite small, and between Martian geology, biology, and climatology, severely overworked. Venus is a boiling steam-bath with weird metal-eating micro-organisms floating in the dense atmosphere, and all sorts of vast and weird critters float in the atmosphere of Jupiter: Europa, Jupiter's moon, also has life in the seas beneath its icy crust, clustered around the warmth and energy-rich minerals which escape from the many sea-floor rents and volcanoes (Europa is twisted hard by Jupiter's tidal forces, if not so much as ever-exploding Io).
The Moon is the same heckhole as in our universe, the discovery of some very odd rock-like, radiation-eating "plants" (later found on some of the asteroids) nowithstanding. The international lunar base is the largest off-earth settlement, and the Farside observatory a major center of astronomical research. The lunar base, some twenty-seven years after it's founding, is getting quite homey: it now grows most of it's own food, and has a large number of families with children: the first child was born on the Moon back in the late 80's. For the wealthy, going to the moon and back nowadays is essentially a "weekend excursion."
There are a multitude of large space stations in orbit, including three big international ones at the geosynchronous points and rather more in closer orbit: at any one time there are several thousand people living and working in space.
Global warming is a more controversial theory than in OTL, because the effects of human modification of the atmosphere are being masked to some extent by an ongoing decline in solar radiation. In fact a new ice age is in the offing, and if people don't stop building nuclear power plants and start burning more coal, things could be getting downright chilly by the end of the 21st century.
The USSR is still around, having slowly reformed itself economically starting in the 60's, it's leadership being less blinkered by ideology and a bit more "scientific" than the men who ran it post-Stalin OTL. Eastern Europe is not an issue: the states of the Warsaw Pact have been steadily assimilated into the USSR, and the current Supremo is a Bulgarian. (The Poles, admittedly, remain rather grumpy and rebellious). Although it's economy is more Capitalist than Socialist nowadays, the USSR is still a one-party state, which justifies it's existence as the one true post-nationalist state and the only country where the improvement of all mankind, rather than the pursuit of individual wealth, is the true common concern.
The USSR holds itself out as a champion of third-world development (more successfully than OTL: the mere addition of "socialist" kleptocrats to "our" side to win propaganda points is considered below the dignity of the Soviet people, and the USSR invests heavily in Africa, S. Asia, and Latin America admittedly, cynics claim that this just means that third-worlders get to be exploited by run-for-profit Soviet industrial combines rather than run-for-profit Western corporations.) It also has made some good propaganda points with it's recent massive investment in post-fossil fuel technology, and contrasting it with the lackadaisical response of much of the western world. It's also a rather less sexist place than OTL Russia, which is perhaps one reason for a higher birthrate.
The Cold War is now the Tepid Truce: the US and USSR may still compete for influence and trade, but arms limitation treaties were in place by the 70's, and both sides have been on low alert, militarily speaking, since the early 90's. UN arms inspectors and lots and lots of spy satellites keep both sides honest, and the current odds of an accidental nuclear war are practically nil: still, the capacity is still there, a fair amount of national muscle-flexing occurs, and on both sides of the Atlantic writers of Technothrillers cheerfully imagine futures in which tensions have returned to the good old days of the 60's.
(Not that the Soviets don't have their paranoid side as well. They still have a chip on their shoulder about being Number Two, and it's not just the US that still has some hidden atomic weapons in orbit.)
The British Commonwealth is an institution which still has some juice in it. The UK, Canada, NZ, Australia, Singapore, and various other places remain closely tied in a free trade block with a common military, space program, etc., and the UK, rather than going the services-and-de-industrialization road, has remained one of the "Workshops of the World", along with Japan and Germany. The UK is one the whole more "lefty" than OTL: Margaret Thatcher never arose to national prominence (although nuclear power ended up putting a load of coal-miners out of work anyway), and Business Administration grads and Total Quality Management types are thinner on the ground. Australia and NZ are more populous than OTL, and Australia is one of the world centers of the space exploration biz: although the Commonwealth space effort is increasingly one of junior partnership with the US, it's a partnership and the Commonwealth did manage to land it's own ship on the Moon.
India, rather estranged from the UK in the 50's and 60's, has since patched up relations, and has increased economic and technical connections with the Commonwealth, although it has not become a full member (unlike Sri Lanka): this Has Been Noted in the USSR, which has worked hard to woo back the Indians with a variety of technical and scientific aid.
China remains far more Marxist than OTL, and looks like more like the late 60's USSR writ large than early 80's S. Korea writ very large. It's not N. Korea (in this world kept afloat by Soviet subsidies) the population is fed (tolerably, if rather blandly: the Chinese are the world's leading experts on synthetic food production) and there's a substantial free market, but the Commanding Heights of the economy are still very much under the control of the government. It's also rather hostile to the Reformist Capitalist Lickspittles of the USSR, and is not particularly loved by the US. Given it's distinct disinterest in Capitalist mores and regulations, China has not only been the world's largest producer of satellite TV pornography, sleazy "exposes" and bloodsports since the late 60's, it's since become a heaven for "offshore banking", smuggling, video piracy, etc. not to mention the whole drug trade thing. Initially this sort of thing was meant to undermine the capitalist system, but in the long run it's just become a way for the Party elite to fill their pockets.
The EC is doing OK sans British participation, although this also means (the horror!) that the French dominate the show.
Japan is a major industrial power, but in a world where the US, USSR, and Commonwealth have all done better than OTL it has never scared any of the bigger powers, and remains somewhat of a US satellite, especially in the face of a China somewhat more alarming than ours.
Africa is doing a bit better than OTL thanks to more investment, better development economics, and a bit more luck with it's governments: it's stable enough that the world's largest radio telescope is here rather than in Latin America. On the down side, Apartheid in S. Africa has come to an end much more messily than OTL.
Islamic fundamentalism is less influential, secular nationalism more powerful in the Middle East. Egypt has managed to modernize it's economy more successfully than OTL, the Iranian revolution failed, the USSR stayed out of Afghanistan and the current dictator of Iraq has successfully avoided getting into fights with any of his neighbors. Israel avoided the poison fruit of the West Bank, although all of Jerusalem is currently incorporated into the Israeli state.
The US is still the world's number one power, although it's a more multipolar world than ours. The US avoided Vietnam (although it did get into a few messy little actions in Latin America and Africa) and never suffered the severe malaise, or the excessive counter-reaction, of OTL 70s and after. It's a more secular country than OTL, although also a less cynical one. There's a lot more tolerance of gays and lesbians, and they are allowed to marry in most states outside the Bible Belt; the first Jewish president was elected in 2004. The air is cleaner, TV is dirtier, and political discourse not much more elevated than OTL, if slightly more related to the real world on an Earth where the Conquest Of Space does provide something of a actual national Grand Mission and the country has some powerful competition (if no longer outright enemies) rather than some batshit guys in a cave.
In a small temple in the Himalayas, a curious Buddhist sect continues to write all the possible names of God. There was some talk of getting a printer and a computer to speed up the work, but the chief monk laid down the law about offending God by turning a labor of devotion into a vulgar mechanical process.
Transportation is not too different than OTL, although there are more trains, electrical cars are more common, and there is a surprising amount of hovercraft travel. One notable difference is that given superior rocket and aerospace technology and enthusiasm for speed and fancy machines the supersonic passenger jet has done rather better, and a two-hour NY-London flight is the norm.
Technology is more advanced than our world in several fields. Aside from space travel, there are also advances in chemistry and materials sciences, which has yielded some ultra-strong construction plastics and super-strong carbon-fiber wires and ribbons, and biotech: the Soviets are especially advanced in the creation of GM plants for surviving in harsh climate conditions, and are currently trying to develop plants capable (given a little water) of growing on the Moon. Japanese scientists are trying to tinker with chimpanzee genes to increase brain growth: Soviet surgeons have successfully given some apes vocal cords, with disappointing results. A form of sleep-hibernation for space travelers has been around since the mid-90's.
High-quality synthetic diamonds are cheap: De Beers has gone out of business, and the more chemically complex (and expensive) emerald has become the new favorite for rings.
Computer science is also more developed: the first AI computers were developed over the course of the 90's (one might say they "grew up" ), and one of the early models went along on the 2001 US trip to Jupiter. There's an internet, as OTL, if more heavily regulated: there are a _lot_ more books online than in our TL, though. (Copyright law failed to be extended as absurdly).
Antigravity (and, for related reasons, time travel) are both possible within the physics of this universe, but nobody has any notion yet of how they might be achieved (at least, as far as anyone knows
Great steps have been made in the interpretation of the language of dolphins, and lemmings actually do occasionally stampede en masse into the ocean. Scientists have no idea why.
The US, USSR, Commonwealth, and other big powers have stepped in to put an end to the overuse of dwindling stocks of marine food animals, and the International Fisheries Organization has real muscle. Ambitious scientific schemes to restock the oceans and cultivate marine life in an organized manner are being considered.
Culture is a bit more staid than OTL. Rationalism and scientific thinking are a rather more popular outlook, and Improving Programs, Science TV, and interplanetary exploration sagas abound. Carl Sagan (who in this TL lived until 2007) got to do more big-ass TV science shows than OTL, and one of the most popular new talk shows is filmed on the moon. Classical music is doing well, and a generation of young composers are trying to create "Music for the Space Age."
Science fiction is more popular than in our world, having less of a whiff of the geek about it. TVs are big and get a great picture high definition TV has been around for a while, in 3D for that matter. On the down side, the variety show has somehow survived.
Flatscreen images are good enough that the "picture window" a crystal-clear image of some distant, and more scenic location- is popular in many homes.
After the strange events which took place during the first expedition to Jupiter, a joint US-USSR mission left in the summer of 2009 to recover the records from the now abandoned ship. The Soviet are providing the ship, equipped with a new fusion drive (the "Sakharov Drive") that will bring the expedition into Jovian orbit within a couple months.
Meanwhile, those whacky Chinese have launched a nuclear ship in hopes of beating the US-Soviet alliance to Jupiter - a suicide mission if they don't succeed in aero braking on Jupiter and then refueling on one of the Moons. On Earth's Moon, a black monolith continues to baffle the best efforts of scientists from around the world to pierce its impenetrable force-screen. (Some have begun to grumble that they should use a nuke on it). Beneath the ice of Europa, weird, many-tentacled intelligences, fully sentient if confined to a stone age technology kit, huddle around the warmth of a hundred-mile long deep-sea rift which is all the world they know. And in low orbit around Jupiter, a greater monolith, miles in length, awaits