Although moderators are necessary in most nuclear reactors this does not mean to say that all reactors require moderators. There is a special class of reactors known as fast reactors which do not use moderators but depend on the use of fast moving neutrons for causing fission. Even otherwise it must be remembered that fast moving neutrons have lesser probability of getting absorbed and causing fission but it does not mean that they are incapable of causing the fission reaction. Just to give you a relative idea a fast moving neutron travels with a speed which is nearly in the region of 10% of the speed of light, while a thermal neutron travels with a speed which is typically of the order of a few kilometers per second.
There are also other categories of neutrons based on their energy levels such as slow neutrons, cold neutrons, ultra cold neutrons and so forth.