Humans will, with rare exception, live as long as they want. Immortality will have been a fact of life for several decades. How this came about is a bit harder to predict - I feel that either nanotechnology or genetic engineering will be responsible for huge medical advances, but I strongly suspect that one of the two will be rejected by society as something that shouldn’t be tampered with, I just can’t say which. People who think life is sacred and we shouldn’t tamper with it will be for using nanobots to maintain our bodies in perfect health, people who are against the idea of having microscopic robots throughout their body and/or fear the possible consequences of runaway nanobots will favor a more organic solution. Either way, we will tackle natural death sometime in the next few decades.
If we develop medical nanotechnology I predict there will be a pill you can take that will change your gender, or other aspects of your appearance. If we take the genetics path the same stuff will be possible, though it will be via surgery and cloned organs. I think a sizable percentage of the population will take advantage of technology to modify their body, while many people still think there is something wrong or even perverse in doing so.
The idea of having to work for a living will be considered ridiculously old-fashioned, increased automation will be able to provide a standard of living that is superior to that of today’s world’s richest in most ways (though there will be some who reject this new wealth for personal or cultural reasons). People will occupy themselves by trying to gain recognition and fame for their achievements, whether they are artistic, athletic, or whatever. The only resources not available to all will be space and followers, and the most influential people will compete among themselves to have the best of both.
There will be a rapidly growing number of people living in space. Though space travel will never be efficient or popular enough to put a dent in the Earth’s population it will be an option for those who do not want to live on Earth and those who relocate will breed faster. A vast majority will live in orbital habitats though some will live on or under the surface of most planetary bodies in our solar system. We will have some people who have modified their bodies to be able to live in hostile environments, while most will modify where they live to have near perfect living conditions.
Computers will be able to simulate sentience so well that they are indistinguishable from humans if they want to be. Brain-computer interfaces will be advanced, common, and nonintrusive. Computers will have been able to read our minds so long that we will have already worked out most of the ethical problems and reached a point where an acceptable degree of privacy is maintained. You will be able to connect your mind to simulated realities so vast and detailed they are nearly indistinguishable from reality. Many people will choose to live in such a state, and this will be encouraged to save living space.
If we continue to develop biotechnology then we will have resurrected hundreds of extinct species. Many off-planet colonies will have bizarre and complex ecosystems made up of life natural, extinct, and/or wholly man-made. An effort will be made to preserve something resembling a natural ecosystem on Earth, however, and those who want something more interesting will either go off-planet or into simulations.
We will have send unmanned probes to dozens of nearby stars and manned ones to a few. Constant boost spacecraft will be fairly common and you will be able to travel anywhere in the solar system in a few days if you are willing to sleep through a high-G trip while suspended in fluid. Most travellers will prefer more leisurely craft that make a trip to Mars take a few days and a trip to the Oort cloud a couple of weeks.
Well, that’s the way I see it, unless there is something totally unexpected that slows us down or shakes things up totally, like a major war or contact with aliens. In another hundred years things will be almost completely the same, except that the vast majority of the solar system’s population will be non-Terrestrial and there will be colonies in other solar systems.