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There are quite a few ways to generate electricity without burning fuels, among them solar, wind, hydroelectric, and geothermal.
Hydro and geothermal can produce electricity at a constant level like a nuclear power plant, and can ramp up or down to match demand, like a fossil burner. But hydro requires a river and has its own negative environmental consequences. Geothermal is only economically feasible to implement in certain places--though this may change if fracking-originated deep well technology is applied to it. But that's another story.

So for the moment, the most widely applicable means to cleanly generate electricity are wind and solar. But these generation sources have a problem: they only produce electricity intermittently. A few solutions have been found, including pairing them with peaking fossil burner plants, adding battery storage, or overbuilding them to match peak demand during the period of lowest production.
Using supplementary fossil burners is an economic dead end; new solar and wind plants are already economically competitive and in some cases cheaper than fossil burners. Most new electric capacity in the USA is renewable, not fossil. Storage is an option, but it's more expensive than simply overbuilding more renewable capacity. So that's what's happening, by and large.
Think about what this means: we will wind up producing excess electricity most of the time. And not only will we, but we already do! In many electricity markets, a fraction of renewable capacity is simply shut down during periods of peak supply because there isn't enough demand for it.
Think about that. We shut down some of our electricity supply because we produce so much more than we need. This isn't a fantasy; it's already happening. All over the world.
Now, that seems wasteful. If we overbuild capacity to meet peak demand during the lowest-producing periods, we'll wind up with tons and tons of wasted electricity during the highest power-producing periods. Resources gone to waste.
But... what if it wasn't wasteful? Right now this electricity is basically free. That means we could install and operate free air conditioning for people who don't already have it. It means free medium-distance mobility for people with electric vehicles. It also means free hydrogen production. And what can you do with hydrogen? Burn it as a fuel in vehicles where the power-to-weight ratio of battery storage and electric motors is not high enough to displace fossil fuel engines. So we could put that hydrogen in planes to have zero-pollution air travel and air freight with essentially free fuel. We could do the same for tanker ships. We could store that hydrogen and use it later, just like batteries. And speaking of batteries, they're becoming cheaper all the time.
It's hard for me to avoid the conclusion that we're rapidly reaching a point in human history where energy itself actually does become "too cheap to meter." This turns everything on its head because our entire economic system is based on scarcity. So what happens when one of the economic inputs to that system becomes non-scarce?
Interesting times.
Now, this is just electricity of course. Raw materials and skilled labor will still be scarce. But unskilled labor is not as scarce as it once was. It's not just immigration from poor countries; automated production horns in on it as well. What happens when recycling reaches a point where raw materials are super cheap too? This is something to get excited about, not to fear!