For conventional piston engines on fire, you generally remove the fuel source (mixture-->cutoff, fuel pump off, etc.) and continue cranking. This will draw any remaining fuel through the parts of the motor that are designed to cope with high temperatures. Having the throttle wide open at this point allows the most fuel/flames to be drawn through and replaced by plain air. You can then rush round with a fire extinguisher, just in case!
The induction systems on some engines, especially if they have air filters, are not so sturdy and may start combusting themselves if exposed to burning fuel. Then you have a problem! (I've watched an aircraft burn down to ashes after this happened.
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A common cause of fires is overpriming, so the inlet manifold has fuel sloshing around inside. A "backfire" at low RPM can push hot/still burning gases into the manifold/filter and set them on fire...