Forget rockets, ion drive, and warp drive. In Star Wars we see the X-Wings being fueled by lighted hoses (or something – it’s been a while). Luke Skywalker’s landspeeder has engine pods that need some sort of fuel. I think Heinlein mentioned nuclear-powered vehicles in some of his stories. That seems quasi-plausible, given the era when Heinlein wrote those stories, and given that that sort of ‘nuts-and-bolts’ stuff is usually not important to the narrative. IIRC, The Cold Equations used a regular old rocket-powered vehicle, and the Moon vehicles in 2001 used reaction jets that used developments of existing technology. But for the most part, authors say something about nuclear power, hover-drive, or something and leave it at that. Have any science fiction stories actually taken the time to explain the power source of ‘non-space’ vehicles? And by ‘non-space’ I mean vehicles that are not designed for interplanetary travel, though they may travel in space. For example, landspeeders (Star Wars, non-atmospheric vehicles (2001 Moon shuttles), and various terrestrial vehicles.
The Wind-up Girl posits a world with virtually no use of fossil fuels, and many vehicles are powered by fancy springs. Are you looking for something higher-tech than that?
Stories? If you include books, then yeah.
Hammer’s Slammers (David Drake) AFV’s are fusion powered air cushion vehicles, Hammer's Slammers series - Wikipedia although there are still plenty of (cheaper) fossil fuel vehicles around.
Bolo tanks (originally created by Keith Laumer) are advanced automated tanks. Original (MkI) Bolo’s were diesel, but the MkIII operated on some kind of fuel cell. The later marks were capable of centuries of operation. Bolo universe - Wikipedia
Back to the Future – “Mr. Fusion”.
Never heard of that one! I’m not looking for any particular power source. I’m looking for something more along the lines of this: ‘Harrington eyed his fuel gauge nervously. The Victor & Simmons motor in his hovercar hummed nicely as it provided power to the anti-graviton generators that kept him aloft – but it took a lot of fuel to run it. The fuel was [something], and the V&S motor converted it by means of [somehow] into [a form of power necessary for generating anti-gravitons]. The [somehow] works like this: [technical explanation that sounds plausible in context]. Good thing the fuel packed enormous energy into a small package. But it was about to run out.’
It’s easy to use ‘magic’ – to make up some gobbledygook that serves the purpose of the narrative. But I’m curious if anyone has tried to speculate a fuel and propulsion system that’s scientifically plausible. (At least scientifically plausible enough that an actual scientist might look at it and say, ‘Hm. I wonder if we could actually do that?’)
mlees: Those links look promising. I’ll look at them later, as I need to start crunching data. Thanks.
Heinlein’s Shipstones.
Stephen King’s book the Running Man featured air cars…which unlike most SF vehicles with that name, are not flying cars. They are normal wheeled cars, powered by compressed air.
He never actually addresses the limitation this puts on their range, that I remember. And, he doesn’t go into how they work in detail, but…they’re powered by compressed air…it’s not that hard to figure out at least a couple theoretical methods to work that.
I don’t recall if fuel supplies ever really become a concern in David Drake’s Hammer’s Slammers novels.
The Bolo stories are more of a collection of short stories centering around a commonly agreed upon premise, and there was one story that I can vaguely recall where a Bolo was low on power, and still trying to fight it’s way to some objective, trying to manage it’s power reserves by shutting down various systems, and so on.
But generally, these (fuel shortages) are all plot devices to introduce tension. An author generally doesn’t deal with minutae unless it advances a story. While good logistics are (one of several) key to victory, most novels don’t focus on Sgt. Draper, Quatermaster, Fifth Expeditionary Force, because bookkeeping is boring. 
Poul Anderson’s ORION SHALL RISE is set in the far future where the fossil fuels have run out - I mainly remember the high-tech sailing ships and I think he had airships as well (not sure how he justified those); the book itself as I recall had a lot of interesting ideas but the plot kind of dragged on and on.
Energy supplies do come up a number of times in the Bolo stories, when they are operating on* “X percent of reserve power”*.
In Vernor Vinge’s Run Bookworm, Run! the fact that the engines of vehicles don’t need fuel is a way of bringing up some of the setting’s history; massive economic dislocation occurred when a cheaply mass producible fusion plant was invented that could run off the hydrogen extracted from water vapor. The entire energy extraction & distribution sector of the economy collapsed.
In In Fury Born one character is somewhat disgusted that the ancient APCs they have to use run on the “grotesque so called technology” of petroleum distillates.
One of my favorite books!
In Deathworld 2, the fuel of the local vehicles as well as how they work (crude steam engines) is important as part of the overarching plot about how the protagonist understands the local fragmented* technology better than the locals do.
*Local technological knowledge has become a collection of poorly understood techniques mostly performed by rote, by many different clans that only understand small specialties.
“Car Wars” was a game whose premise was similar to a Mad Max type of collapsed society, with electric battery powered cars duking it out on the streets and highways of America. A trilogy of books was written based on this setting.
The battles themselves were too short to worry about the overall of level battery charges, but they were rated by acceleration rates for the purposed of combat. On a strategic sense, they had a couple hundred miles range. (According to game supplement materials.)
I only include this because of the (science) fiction novels based on the game makes it qualify as a borderline case for the OP.
You can do most of what a fossil fuel can do with electricity, and there are several ways to get electricity.
There are the renewable methods of solar and even wind. I’ve seen a guy with a windmill blade mounted on a collapsible mast on his car, which he used to power small electronics when he didn’t want to burn fuel. (I’m in California. I see this weird kind of thing.)
There are fuel cells and similar technology which split water using a membrane and use the resulting electrical potential for power. This isn’t production ready technology now, but it’s feasible.
These are near future technology, but I don’t think that’s going to power an anti-graviton anything. For that, you need nukes or better. If you’re already introducing anti-gravitons, anti-matter is an option. As is fusion. For propulsion, you can stick with anti-gravitons (just spit them out in a different direction), or you can add some conventional turbines on the vehicle and propel it like a jet helicopter with lift provided by anti-gravitons and propulsion provided by turbines and compressed air.
And if you want to go low tech, there’s always human power. Instead of the fuel running out, his legs start to give out.
In the Stainless Steel Rat books, there are two of note:
A small boat which takes water in from the front, heats it in a nuclear pile (not a reactor, though) and ejects the heated water through a jet nozzle in the back.
Police motorcycles powered by the stored energy in a flywheel, which itself is spun up overnight.
edit: also, a self-stoking coal-fired steam boiler-powered robot butler…
“Stoke, you idiot! Stoke!”
Unpronounceable, “nuclear pile” is the same thing as a reactor. It’s just an old word for it.
To the OP, are you interested in propulsion, fuel, or both? They may or may not be the same thing.
Quoth mlees:
In the The Fleet shared-universe anthologies, there are a number of short stories (admittedly not full novels) that do star a quartermaster. He’s continually having to Macgyver his way out of enemy encounters using whatever supplies are on hand (which usually seem to involve copious amounts of paint).
Oh, and to the OP, Niven’s later Known Space books (around the time of Gil Hamilton, I think) posit an Earth where fossil fuels are so tightly regulated that surface-to-orbit rockets are powered by air compressed nearly to the point of degeneracy. Personally, I’m not sure I buy that: It seems to me that it’d be easier to use whatever energy source you use to compress the air to instead manufacture proper rocket fuel (either by splitting water, or from atmospheric CO[sub]2[/sub]), and then burn that: If you’re manufacturing the fuel from the stuff it burns into, then the whole process is carbon-neutral.
Is that intended to be comedy/satire?
Yes and no. Nuclear pile is usually meant to mean ye ole reactor de la fissioine
However, there are some short lived hot as shit isotopes that could be used as a heat source for something like a steam engine or jet engine or whatever. The only real problem (besides the expense and the radioactivity) is that the need constant cooling.
So, you could have some isotope powered jet/rocket engine. But it would have to be running continously to avoid melting down.