I don't think the Apocalypse is going to happen, but I wouldn't be surprised if there is another plague that's good enough that it wipes out a good portion of the world.
That, or we have a nuclear war.
I definitely don't think that in 100 years we're going to have any more than 10 billion people, because people will definitely be more conscience about population by then - or still recooping from some sort of dramatic wipeout.
I don't think, though, that even if we had a wipeout, that there would be any real halt in technology. If it's a war, all technology benefits. If it's a plague, then health technology benefits.
I expect people living to 120 years to not be uncommon. 150 will be the extremely rare old coots, though.
Cancer and AIDs will be a thing of the past. We'll have other diseases. But, our health technology would be good enough that people have less risk of dying from disease.
Food technology could also increase the life of a person.
Genetic techology will be somewhere. Where it is depends on legal matters.
The use of stem cells to regrow organs/limbs will either be the main solution to most problems. Or it will be a thing of the past, as we may have better technologies by then. That depends on if we have any big plagues or not.
There will be no communism in any large country. There may be some socialism here or there, but there will still be a lot of personal freedom granted. Most people will still be capitalists, though, as that is the perfect drive for technology advancements, and people will have fully realised that by then. Well, dictators drive technology greatly, too. And we'll probably a couple more Hitlers in the course of 100 years.
But nothing permanant.
I expect that many of the small countries will be absorbed by larger ones during the war/plague. I fully expect Europe to be a matter of only a handful of countries in the future, if it it isn't all one.
South America will be only a handful of countries, too.
USA may absorb Mexico and most of central America. I doubt Canada and US will be the same country, but it will probably be so heavily dependent on each other that we will be equal partners in some great North American Union. This NAU probably has the biggest chance out of any country to have gained lands over the Atlantic/Pacific oceans. Such as Japan, the Phillipines, and Israel. All other countries will lose influence with far lands - such as the British Commonwealth.
Once again, Middle East will probably finally be a matter of a couple countries. It does however have the largest chance out of any area to have even more countries than it does now. There will still be a distinction between Persian and Arabian countries, though - no matter the religion, they will never combine.
Africa will probably have the most countries out of any continent, and it will be dramatically more developed.
Russia and China's borders will probably remain as much as the same as it is now, although Russia may absorb former USSR countries.
China will probably have Hong Kong and Taiwan, though.
It will have Japan if Japan isn't gained by the US/NAU or if Japan doesn't absorb other lands in the Pacific Rim.
Antarctica will probably be either split up between the big countries, or it will have its own country. It will be developed and populated.
I also expect underwater communities to start up, but I don't expect any "floating" cities. These underwater communities will start as resource gatherers, and eventually become cities.
Life as we know it won't be dramatically different, though. People will still go to work, still have some sort of personal transportation, still do recreational activities, and most countries will have some sort of personal freedom.
There will be a space race once again. And it will be very, very good for us.
It won't resort to warfare, though. It may have in the past, but by then we'll be over that.
We will definitely have a new propulsion system by then. It will be because of this new technology that we will finally have a good, new source of energy for use in cars.
If there isn't warfare in the space race, we will definitely have resorts in orbit.
The moon may be populated, even if it is only by government officials from countries on Earth. I seriously doubt the moon will have its own nations. It will be a major refueling station, though.
Mars will probably be our main focus of interest - though by then we will have begun major exploration of the asteroid belt. We may even be mining by then - in fact, I expect us to be asteroid mining by then. Mars may have a base or two there, and it will act as yet another refueling point. Most research will go on there, but people will only live there for six months at a time or so. We will have no one near Jupiter, yet, but we will probably have a ton of probes exploring it.
We probably won't have anyone on Venus, either, but we may be trying to figure out how to harvest minerals from Venus.
And as for actual warfare, though - we'll be using video gamers. All military vehicles will be remote controlled. Soldiers, if we have them, will be remote controlled robots - we will NEVER have AI military. Actual humans will be safe in some bunker somewhere, playing video games against each other.