There are different types of nuclear reactors.
The most commons ones are pressure water reactors and boiling water reactors. The World Nuclear Association has published the following information:
Pressure Water Reactors (PWR) are currently used in: the US, France, Japan, Russia & China. The number of such reactors is 277.
There are 80 Boiling Water Reactors (BWR), predominantly in the US, Japan and Sweden.
Both PWR and BWR type reactors use enriched uranium for fuel and ordinary water as the coolant.
Additionally, there are 49 Pressurised HEAVY Water Reactors (PHWR) used in Canada and India. Unlike PWRs and BWRs, these reactors use natural uranium as their fuel and heavy water as the coolant.
Other types of reactors that have been used are Gas-Cooled Reactors, of which 15 where constructed in the UK. These reactors used natural and enriched uranium for fuel and carbon dioxide as the coolant.
The Russians have also built 15 Light Water Graphite Reactors which use enriched uranium for fuel and ordinary water as a coolant.
The Germans and Russians have built Fast Breeder Reactors which use plutonium and uranium as fuel and liquid sodium as the coolant.
Stanford University provides additional information about reactor types.
The next thing to appreciate is the fuel assemblies used in nuclear reactors. The fuel for PWR, BWR and PHWR reactors (the most common currently used reactors) is uranium oxide powder that has been formed into small cylindrical pellets. The pellets are then placed into rods. The rods are then assembled into bundles and bundles are brought into close proximity to other bundles in the core of the reactors.
Fission within the reactor core is via neutron interaction between the pellets in the rods, the rods in the bundles and between the bundles.
To effectively stop fission and heat production, the bundles would have to be separated to prevent neutron interaction between bundles, rods within bundles would have to be separated to prevent interaction between rods and pellets removed from the rods and separated to stop interaction between pellets.
This is impractical for general operations and is only undertaken when a core has to be shut down so spent fuel can be replaced. Its why moderators are used and why coolant must be continually supplied to the reactor core to control neutrons and the rate of fission and heat generation.
If reactors are deprived of a continual supply of coolant for a prolonged period the core will overheat. Depending on the duration of coolant deprivation, the reactor structure may be damaged and environmental contamination may eventuate as happened at Chernobyl in 1986 and Fukushima in 2011.
These are extreme cases and it is why the restoration of cooling, as quickly as possible, was a very high priority at the stricken plant at Fukushima, even though they were unsuccessful due to the extensive damage at the plant.
The critical factors in whether there will be radioactive contamination resulting from coolant deprivation of a reactor core is the design and construction of the plant and the duration of coolant deprivation. Deprive a nuclear reactor of coolant long enough and contamination will occur. Nuclear reactions produce a lot of heat.