This is a tough crowd!
Just some statements off the cuff as pertains to I.C. engines.
First, "The High Speed Internal Combustion Engine" by Ricardo 1923 IS a MUST READ!
Gasoline engines don't need spark ignition to burn, but the uncontrolled flame front propagation will kill the engine in no time.
Honda experimented with "Radical Burn" technology and there are several "lean burn" schemes that have come and gone over the years. (as mentioned here by others)
Gasoline engines also rely on the "heat of vaporization" to cool the intake charge.
Alcohol burning engines such as JAP or ESO speedway machines run VERY HIGH compression ratios without detonation due to their FUEL, Alky, but still rely on spark ignition.
Methanol is Alky, and has a HUGE heat of vaporization value, Speedway bike cylinder heads are sometimes insulated to keep heat IN.
Popular in England , and elsewhere for a time, were TVO engines. Thermal Vaporizing Oil.
The spark ignition engines were started on gasoline, and after a suitable engine warm up, the fuel tap was switched to draw from a kerosene tank. This was popular for ag tractors due to fuel costs and availability. Many Fordson tractors built in Cork and Dagenham were so fitted.
This "flex fuel" desighn was an option for the E27n that I run, though the one I have is gasoline only. IIRC the engine compression ratio is around 6:1. ;-)
There was little difference in the engine internals between the TVO and a gasoline only engine., but the induction track had a Heat Plate that was warmed by the hot exhaust. I'm quite sure the engine would run just fine on gasoline but perhaps there would be a tendency to knock under load.
I am not aware of any Diesel cycle engines that do not make use of direct injection. The pressurized spray being required to atomize the heavy fuel being necessary I suppose.
Ocean going diesels burning "bunker crude" require fuel heaters to liquefy the fuel to make it suitable for injection.
Compression ignition engines Diesels, come in both four stroke and two stroke designs.
The "Detroit Diesel" the flag bearer of the two stokes.
I have not seen any "rotary piston" compression ignition engines . Wankels would seem to be a great platform, but not yet ;-)
I could go on, Please add in any otherr gems you might be holding back. I have engoyed the IC engine all my life, I must have 40 of them all counted .
Now don't get me started on glow ignition. I can smell the "Missile Mist" now.... ;-)