Imagine the population of our planet is given free (almost) and unlimited energy.
What kind of technologies would go mainstream which are not feasible today due to prohibitively high energy requiremnts? What would happen to our environment with 12 billion humans 'high' on unlimited energy? What would our planet end up looking like when obeserved from out space? Would 'everybody' end up owning a space ship?
With that much energy, it only takes one idiot to melt the Earth. On the upside, we'd probably be godlike by our present standards, so humanity will have long before diffused across the universe.
By the standards of a century ago, that's the world we're living in.
By the standards of a century from now? Who can say.
Imagine a world where a horse is the ultimate source of power, let's call that one horsepower (1 HP, 745.7 Watts). A horse can do a lot of work but not fast.
Now take a person who knows only horses and put him in front of the engine in a cargo ship (81 MW, 108623 HP Emma Mærsk) and tell him we're not living in an era of cheap almost unlimited energy.
Large-scale recycling would become feasible and cost-effective.
Recycling currently has a high cost: picking and sorting refuse, transportating refuse to a recycling station, and transforming it (chemically, physically, biologically) to something usable by the industry. With much cheaper energy, the two last processes cost much less: heating, cooling and moving, useful in all transformation industry, are energy-based.
Recycling, by its turn, would solve a bigger problem: scarcity, and one-source dependency, of some natural resources, like rare earth elements. And that would shake the world's geopolitics.
All of these things combined lead to...
Unlimited and (almost) free energy (in a form that is directly usable, from a wall socket or a fuel station) has fantastic potential. Ideally, it woult change earth into a post-scarcity society.
Practically everything comes down to energy. The food we eat is chemical energy, and required energy in various forms to grow, to be harvested, transported and processed.
Heat is energy, as well as light.
Every object you possess was made using energy.
So, in short, with (almost) free energy, almost everything is almost free, too.
The only potential problem is that whenever you have people, you will always have some who want to have more than others. That means tehre will be some people who would prefer if not everybody had everything they need for free.
But personally i hope that the availability of a post-scarcity society would get enough people to defend it from those too greedy.
EDIT
Following @sdrawkcabdears question:
With that much energy so cheaply available, and provided that the benefits of this are not pinched by a small group, it seems safe to assume that global birth rates will drop. This follows an observable pattern that shows that the more educated women are, the lower the birth rate. Education is easier to get once you have energy.
With lower birth rates one can assume that global population will not grow too much from current levels.
As a result, the amount of things people need can be regarded as limited.
With enough energy very cheaply available, mining, refining and recycling operations get easier.
The (finite) global population will never need an infinite amount of things, especially when you recycle the waste. So, having enough of everything for everyone boils down to having enough energy and a few hand fuls of smart people coming up with handy ideas about how to make the things people need. This part should be laughably simple, when you have 8 billion people who are not fighting for their survival.
It very much depends on what kind of energy it is, and what we do with it. Unlimited energy means it has to come from somewhere, and go somewhere.
Solar is the obvious candidate for an unlimited energy world, with the day far away when we ever have any scarcity of solar. But that doesn't mean we'll have unlimited resources of everything else and 100% efficient machines.
Even if we assume every single machine runs on electricity which we can cheaply convert from solar, they'll dump heat into the atmosphere, driving up temperatures. Also, demand for materials will shoot up which enable us to store and utilize electric energy(such as Li-ion batteries).
On the bright side, comfort level of people will increase. Today electricity can be converted to almost any other form of energy - heat, cold, magnetism, fuel, anything. That'll help people get comfortable where they live - and it'll be widespread as even the poor will be able to use the energy.
Mankind will have a more sustainable future than what is there today. We could control or even reverse the greenhouse effect, reduce pollution and eventually eliminate it, build high speed transportation to anywhere in the world, build energy based shields for large scale disaster control.
Another use I can find is high-speed space travel. Assuming we can store and use huge quantities of energy in spaceships(developing the ionic engine concept), we could achieve near-lightspeed travel. That could allow us to inhabit and mine other planets.
So to summarize, it could lead to elevated temperatures(atleast unless we find a way to dump that excess heat), put a strain on other resources as the resource use per capita increases, but aspects of life dependent mostly on the energy we use will see a significant benefit.
user16295 has a great answer. Availability of energy is one of the most important things for technological progress. So unlimited energy will boost our technical capabilities. We would start heavy space travel, maybe terraform Mars, we would build huge buildings and ships. Basically everything we would do anyway in the future.
So the answer to your question is: the word would experience a very fast technological progress.
Some follow up questions to consider are: how will the unlimited energy affect earth? This depends on how we produce it. Out of thin air? probably not. Will environmental pollution and destruction be a thing? will we get the energy from other celestial bodies? Is the energy transportable? (it helps nothing to have an fusion reactor sourcing a bazillion terrawatts if you can't fuel your spacecraft with it)
One practical thing that occurs to me is the usage of aluminum. It is more abundant than iron, it has higher specific strength than steel, it forms a oxide layer which prevenst from rusting, it has a lower melting point making easier to work with and it is easily recyclable. The biggest problem with aluminum production is the energy necessary to extract it from its mineral. Having that solved, imagine:
Buildings done with aluminum alloy could be easyer to built and could be taller,
aluminum bridges without necessity of being painted, light cars, ships, trucks, trains, etc.
And all that without much of oxidation and recyclable. Cheap aluminum alone would make the Earth way more abundant.
Tagging on to some of the other answers, having cheap, unlimited energy would be a great boon for technology. The part that hasn't been mentioned, however, is the finite level of other resources. One of the main issues your new world will have is figuring out what they are using to make the physical objects. Yes, we can travel to space using the new energy, but we still need steel and iron and all of the other materials that go into creating a space ship.
You are going to have a lot of waste from people determining how to convert current objects to use the new energy. The form that the energy takes will determine how many different products need to be adapted (cars, for instance, will almost certainly need to be changed to use the new power).
Also, is your new energy clean? Coal, for example, is pretty cheap, but burning it has a lot of environmental downsides. If your energy isn't clean, organizations will either need to enforce environmental standards or the use of the energy will make living more unpleasant over time.
What does thermodynamics say?
As others have mentioned, the source of energy affects the scenario. So let's assume energy is produced by invisible pink unicorns that run around in some fields and just magically put essentially boundless amounts of electric energy into overhead power lines.
Now you're going to use the energy to do something. Since energy is never created or destroyed (pink unicorns notwithstanding), it will not disappear when it's done what you wanted. Instead it turns into waste heat.
Today we use about 700 exajoules per year. If we increase this by a factor of 10 000, the waste heat would be about equivalent to the heat provided by the sun. The earth's temperature would increase by several tens of degrees Celsius (much more than from currently predicted global warming). The earth would become largely inhospitable.
What would increasing energy consumption by 10000x get us? Well, getting everyone in the world to the per capita average level of energy consumption of the United States would increase energy use by a factor of 10x. Increasing it so everyone lives like the richest 1% in the U.S. takes another factor of 5x. If you want to be conservative and leave the earth inhabitable by humans, you can't go much further than that.
Of course, if you maintain (or amplify) global inequality, you can do all sorts of crazy things.
How unlimited is unlimited?
If you're serious about energy being unlimited, then converting energy into conversion is on the table: E = mc2. That's 9×1016 Joules per kilogram. At that point, you can have Star Trek replicators (once the science has been worked out), that can create anything you desire.
If science works out the inverse – converting matter into energy – then it's only a matter of time until someone is crazy or careless enough to create a hundred kilograms of antimatter, and then the Earth is destroyed. But that will never happen, right? All nine billion people on the planet are completely sane.
These are the immediate things which come to mind:
1- Free (very cheap) travel
2- Free electricity for all (includes air conditioning and central heating)
3- Production costs of all things reduced by at least 30%
4- Recycling things would be free hence again reducing costs
5- Our knowledge of particle physics would increase tenfold considering that particle accelerators would work at much elevated energy levels
6- Space travel would get a boost
In general, much much higher life standard than we have now.
I am assuming that this cheap energy is non polluting and delivered to its users as electricity. Also that the generating plants are large things and somewhat expensive (so cheap energy not free energy).
It would make it possible for everyone to enjoy clean water, enough to eat, a habitation that is not uncomfortably hot or cold.
However, although the running of desalination plants, artificial farmland illumination, multistorey farms, heating and air conditioning would become free, capital and people would be needed to build these infrastructures. So don't expect instant utopia. Probably don't expect utopia at all.
The planet will still be crowded. If the human population continued to grow exponentially, we would soon again be facing environmental crisis directly caused by overpopulation, rather than indirectly. However there is much evidence that if you give people a western standard of living and access to contraception they adjust the size of their families downwards. So hope exists on this front.
Don't confuse cheap "free" nonpolluting energy with universal access to silly wattages in tiny packages. The latter is a disaster like giving everyone hand grenades, or nukes. The former just lets you leave the appliances switched on without facing financial ruin.
There will still be wars, terrorists, etc. I don't think not having to pay the electricity bill would make that much difference. Destroy the infrastructures and you can't access the energy. Cue the four horsemen. Not much change at all.
Transport. Everyone could afford a car. Probably battery electric, possibly hydrogen made by electrolysis of water. I'd hope that free public transport was developed rather than tens of thousands if miles of ugly space-inefficient motorways. Hydrogen is tricky stuff to handle but might be the future aircraft fuel. Or one could make hydrocarbon fuel by using algae in tanks and "free" electric lightt.
We'd be able to clean up the environment without the problem that large energy expenditure incurs large CO2 output which could end up making things globally worse not better. Pollution could be much better managed in this future.
