I think personal computing power will continue to increase exponentially, to the point where a device the size of a phone can be more powerful than anything on the planet today, enabling people to simply be more effective at everything they do. The user interface will be intuitive and literally all around us. I'm not convinced that the devices will be merged with the human body but the continued shrinking in size of both computing and input devices will lead to the entire world being saturated with meta-data instantly available through personal computing devices. Brain-wave input devices may or may not work out, but advances in user interface concepts will be almost as good.
As a side effect, the entire way we do business, all types of commerce, will be changed almost beyond recognition. Any buyer will be able to instantly connect with any seller, and all information about both the buyer and seller will be instantly available with no middlemen or paperwork messing up the transaction. Imagine a world full of day traders, except every sale and purchase can be made directly, essentially by simply thinking about something you want/need and approving the final transaction from a seller who could be anywhere in the world. Like amazon.com plus ebay plus wal-mart plus the NYSE plus any other trading group, all accessible and researchable with a simple thought.
And smart people will still take advantage of dumb people... That won't change. And some people will choose to live "off the grid", which will probably become an increasingly unique type of vacation or lifestyle choice.
It's similar to the much talked about "singularity" of human progress, but I think the progress levels off instead of continuing to climb exponentially. It's still going to be interesting.
Oh yea... Now for what will really happen.
The average human lifespan will rise to maybe 100 years, but the last 20-30 years will still suck and be very expensive for most people. Transportation will still be slow and the TSA will have placed naked body scanners every 50 feet on every sidewalk in the nation, because you can never be too safe. The federal income tax will approach 90%, but the budget will be 99% interest on debt and the remaining 1% will be split between the IRS, TSA, and federal enforcement of the DMCA by the DHS, because copyright theft really does threaten national security.
We will not colonize the moon because most people are selfish cowards and those people vote for things like free needles condoms and birth control pills, not space technology research.
Native Africans will have a continent-wide debate about what to do about all the illegal honkeys...er... undocumented caucasian immigrants, when white North Americans realize that Africa has about half of the world's unused natural resources and start swimming/rowing East in search of a better life. Australia will put up a wall around the entire country... not to make it one big prison again, but to keep Americans out. Australians will feel vaguely guilty about this and will respond by trading guns across the border in exchange for cheap recreational drugs.
Russia will slowly dwindle to nothing as their cultural paranoia continues to erode their birth rate well below replacement levels. They won't trust anyone enough to have kids with them, and of course it's going to be the fault of "the West". Again.
The Moeller skycar will finally fly and promptly crash, killing it's 150 year old builder who wasn't having much fun being that old anyhow.
Everyone who is anyone will have nukes, except the US. We will spend Trillions on a large standing army that is widely dispersed and on constant alert because nobody will have any reason to NOT nuke us. We will want to build more nukes, but we sold the mineral rights to our uranium and other rare metal deposits to China and they won't sell any back to us. Fool me once, shame on you. Fool me 1000 times, shame on... hey a squirrel!
We will invent a universally low-polluting source of power, that has one possible hazardous failure mode. After safely using this power for decades, there will be one failure due to a one in a million natural disaster, leading to the death of just one person and a bunch of housepets. This will cause all responsible nations to immediately abandon that power source and return to mining coal and burning gas/oil, which has a known fatality rate in the hundreds or thousands annually, on top of the environmental damage caused by burning coal, gas, and oil. This switch will be widely applauded as a mature leadership decision and anyone pointing out the fatality rate in the coal industry will be villified as satan incarnate and accused of trying to steal prescription drugs from the elderly.
It will turn out that climate change really IS cyclical just like the last bobillion years of geological evidence shows, and we're going to be needing lots of thick coats and wool socks. People who invest NOW in next-generation snow shovel technology will be the next gazillionaires.
Bill Gates' will activate and switch to his 5th clone following his second consecutive death from a sporting injury, this time falling off the top of mount everest because his climb-o-matic self stabilizing hiking boots suffered a BSOD when he reversed direction and started back down. Next time for sure he'll have his guys run boundary checks and trap overflow errors during QA testing.