Taking the categories from wikipedia, here is my full-hearted take on the next 50 years
AI & Robotics:
Computers are still teh suck at both processing and parsing image data and natural language. So forget intelligent or fully autonomous robots as it won't happen in any of our lifetimes. However, robotics will get very good at allowing humans to remote operate machines
That means things like Robotic deep sea mining (coming off the back of advances in the oil industry). Also increasing use of drones for civilian applications (crop dusting, police helicopters replaced by drones, drones for mapping disaster areas)
Agriculture & Biology:
Don't expect any new wonder drugs to pop up any time soon. There will be small, incremental improvements in healthcare and medicine that will slow down degenerative or damaging diseases rather than cure them outright (especially dementia)
Computer modelling will be the silent revolution in healthcare, allowing managers to determine where to target funds to be most effective.
Any sort of drought, fire or flood in agriculturally productive parts of the world will not longer have just an effect on the country/region where it happens, but instead will affect all countries through global food price shocks and general inflation. Urban agriculture and hydroponics will gain traction as a relatively cheap option amongst a mix of other solutions countries use to ensure food security.
Communications:
Quantum cryptography will become prevalent in most domestic communications devices (smartphones, pc's, routers). All private messages will be uninterceptable, which will be good for personal freedom the world over, but also cause massive headaches for security services and police
Computing:
Miniaturisation is reaching its logical limits (transistors can't get too much smaller than they are now). This will mean processor speeds will increase by smaller and smaller amounts. Instead the focus will shift to other bottlenecks and systems will be built to handle the exponential growth in data that the world is producing, rather than providing raw power that most users don't actually fully leverage.
Gaming will become the number one entertainment medium, overtaking films, books, music and tv. However, the emphasis is already switching to increasing the diversity of games, rather than aiming for a few big shiny games. As graphics won't be the main driver of games sales, we won't see computing technology driven to new heights by games the way it has been in the past
Culture and Leisure:
People are already becoming less concerned with pure economic advancement in developed countries, and that will continue, with people taking a more balanced approach to work/leisure as developing nations become developed
Chinese will have a brief spell where it threatens to overtake English as the lingua franca, and the primary language of international business. However, the (eventual) ascent of India as a world power will mean that it doesn't quite come to pass.
Demographics:
The Earth's population will peak at 12billion according to the UN's current estimates. It will then fall back down to around 9billion before leveling off
Developed countries, followed by developing countries will struggle with, but ultimately manage their aging population crises.
People who's work is done entirely on computer, and who have no families to support or particular ties to any one place, will live and work wherever they can get an internet connection. These "professional backpackers" will be sought by cities trying to generate extra income by having these footloose individuals staying and spending in their region.
Energy:
All cars will be hybrid electrical and internal combustion engines, and slowly, the electrical component will become more and more efficient, with less and less oil required. However, oil will not be completely phased out
Oil sucked from the ground will be replaced by oil generated from growing algae in factories.
Solar panels will be installed on industrial and commercial buildings, especially warehouses, to save costs for companies. Agribusiness and shipping will also get big on wind power as a way to cut costs
Solar in space will gain traction with the military and later, via use in disaster relief, will gain acceptance more widely, eventually replacing fossil fuels
Environment:
Deforestation will slow, but take until the world population begins to decline before stopping and going into partial reverse
Biodiversity will drop in most hotspots, but not to background levels, and will still remain elevated in those areas where it is currently high.
Coral reefs in the Southern Hemisphere will move south and colonise new waters that were previously too cold. However, the new areas will not be as diverse nor be as widespread as the areas that die off. They'll be mostly wiped out in the Northern Hemisphere
Tigers will go extinct in the wild and have to be bread in captivity panda style and then reintroduced. Many medium sized animals will go extinct largely unnoticed
Nanotechnology:
Nanobots won't be reliable enough to be used except in situations (like cloud seeding) where scale is more important than accuracy of results.
However, many products will be engineered at a nanometer scale, with the greatest use in removing flaws in materials during manufacturing processes
Politics & Economics:
The world will become multi-polar, with the US being joined by China, India and Brazil as world powers. They will be known as the big 4, or sometimes the big 4+ (where the plus is Europe).
Just as now, there will also be a second tier of powerful developed nations, with Canada, Australia, Japan joined by Indonesia, Mexico and possibly a few others from Africa and South America
The countries in Southern Africa will form a trade bloc similar to the EU, that will include Botswana, Mozambique, South Africa and Namibia. They will be the first African countries to be recognised as truly developed
Middle Eastern countries will also grow in economic clout and development and eventually be able to pressure Israel into opening up the west bank for economic purposes with them. Israel will eventually negotiate a compromise agreement with Palestine that lingers awkwardly into the 22nd century
Saudi Arabia will be forced to (slowly) change its attitude to women by the US electing a woman as its president. This, combined with economic growth in the majority of mulsim countries will change attitudes towards Islam in the west, and Islamic fundamentalism will fade into history
Transport:
(As already mentioned)
Space:
The Chinese will land on the moon, but only in 2035. If by that time, the US seeding of commercial space companies has lead to unsubsidised commercial spaceflight, then the Chinese moon landings will be seen as of mostly symbolic value
India will try to follow suit, but give up and settle for orbital human spaceflight
No humans will go to mars any time soon. Satellites will be placed at Lagrangian points.
Ceres will be identified as an eventual target for a base to take humans beyond the inner solar system
