For my world, I want there to be many types of ammunition due to the world being an apocalyptic-anarchy kinda thing. Mostly land combat, little to no spacecrafts or vehicles. Anyone know any good ones? They can be chemical compounds, launch fuel liquids, element compounds, explosives, or really anything. Just brainstorming here.
Let's have a look at the mechanics of a gun/bullet.
In a normal gun, the gunpowder ignites and creates a lot of compressed gas. This gas then pushes on the bullet, and flings it down the barrel.
That immediately gives us options. Anything that creates a bunch of compressed gas can fling a bullet out of a barrel. The most trivial example of this are air guns, which literally store compressed air and release it suddenly when shooting. Similarly, steam guns use an external source of combustion to create compressed steam and release it into the barrel. You could fuel a steam gun with nearly anything that produces heat: radioactive decay, burning oil, electricity, dropping a chunk of sodium into water, aluminium into lye. The list is long. Side note: I wonder if anyone has ever made a baking soda and vinegar fueled CO2 air gun.... (@Zeiss Ikon points out in the comments that this reaction only occurs at <15bar, so it would not be very effective)
Then there are internal combustion examples like a normal firearm. For this you need the right mix of an oxidizer and a reducer. Reducers are easy - anything that burns: wood dust, coal dust, gasoline, even most metals will burn. Oxidizers are a bit harder, but are still around: chlorine, oxygen, fluorine, nitric acid. The trick is getting the right ratios, and figuring out how to get it into a gun's chamber, amd get the waste products out. A gun fuelled by sodium (metal, reducer) and chlorine (gas, oxidizer) will have to mix a metal powder evenly with a gas, ignite it, and then deal with the cloud of ... salt (yup, common table salt) that is produced. @Hearth points out in the comments that as well as an exothermic reaction, you also want your chemical reaction to produce a lower density (eg gaseous) result, otherwise it may produce negative pressure! So despite sodium/chlorine combustion looking very exciting, it may not be a great propellent.
@biziclop mentions monopropellents - a single chemical that can decay to another in tge presence of a catalyst. He gives the example of HTP (hydrogen perpoxide) which can turn into water/oxygen: 2H2O3 = 2H2O + O2.
Then there are non-combustion/chemical methods. Spring guns, electromagnetic guns (rail guns, coil guns, linear motors with aluminium slugs). I'm sure there are even more methods of bullet flinging if we allow particle accelerators and lasers as suitable components of our weapons (use a chemical laser to compress a tiny sphere of uranium for a small nuclear explosion in the barrel of your gun. Probably really hard to find ammo for though...).
The list of ways to fling a bullet downrange is, well, enormous. It's jist limited by your creativity, scientific knowledge, and materials available to your characters.
At one point, pneumatic guns were considered a serious alternatives to gun powder powered guns - weapons like the Giradoni Air Gun and Pirchard's air gun. Modern air guns get around many of the issues - you have better/cheaper air compressors, standard pellet calibers, and can be lethal. A world war 2 spin on the design was used as an anti aircraft gun and could launch arbitrary ammunition.
With the post apocalyptic settings - an air compressor could be powered by alternate sources, and such a weapon might be a pre acocalypse holdover or one jerry rigged with items like a fire extinguisher and plumbing fittings. Ammunition's basically castable if they're lead pellets, and reusable. Or you could have your protagonist/antagonist running out of air at the worst time and pumping frantically.
You might also consider an 'pnumapunk' setting with other machines also being air powered.
There are literally hundreds of ballistic propellants. They can be based on any hypergolic chemical or any pair of chemicals that combine to create an exothermic reaction.
This list has only a few.
There are some under research.
There are alternatives to firearms.
DTIC has a freely available database of common pre-modern propellants (useless without specialized knowledge).
Gunpowder suppliers offer guides to different powders.
You'll find a lot more with a cursory search for propellant loads performance, but they'll be manufacturer specific.
How about Biogas?
rotting shit and veggies decomposing biomass like animal excreta, dead plants and stuff like that can actually be a powerful propellant for your bullets. Biogas's composition is basically just natural gas, albeit with a higher concentration of carbon dioxide, hydrogen sulphide (aka the stuff that smells like farts and rotten eggs), and a tiny traces of nitrogen.
Biogas has been shown to have a really high calorific value. Even raw, unrefined biogas has a calorific value of about 30 MJ/kg, with the refined, enriched version of biogas peaking out at 45 MJ/kg. For comparison, natural gas has a calorific value of 50 MJ/kg..
Best part of all, biogas is completely FREE. You can simply get it from
rotting poop and ded stuff animal excreta, vegetable waste, hay etc etc . Basically, any biomass stuff can be used for making biogas.
A big problem is the fact that biogas, like natural gas is explosive. There is a reason why conventional weapons (excluding some exotic cannons and railguns) do not use natural gas/biogas for propellant. Just a bit more natural gas and your gun will shatter in your hands, rather than shooting the bullet.
However, considering the fact that this is your world and you are designing it, you can design a weapon that can use biogas for propellant. There have been uses of gases like hydrogen, methane etc. in Combustion light-gas guns, which are basically gas-powered machine guns. They use HHO (Hydrogen-Oxygen mixture) for propellant, however other choices like methane (Basically Natural gas) can be used. Biogas, considering the fact that it has a closer calorific value to natural gas, can be used in these CLGGs. For now, CLGGs are bulky and immobile, however as it is your world, you can design them to be mobile and portable, and easy for usage in war type scenarios.
Invest in biogas-guns for the future!!