This report has volatile references. Author must fix. - RBL
The heat released by fission in nuclear reactors must be captured and transferred for use in electricity generation. To this end, reactors use coolants that remove heat from the core where the fuel is processed and carry it to electrical generators. Coolants also serve to maintain manageable pressures within the core.
In order for the coolant to work effectively, it must fulfill a number of key specifications. Most basically, it must have efficient heat transfer properties. The coolant must also be a fluid that can fill the interstices of the core and be pumped to a steam generator or turbine. Thermal and material compatibility are vital as well; the coolant should be chemically stable at high temperatures, non-corrosive and a poor neutron absorber. This last parameter is achieved by ensuring that the coolant has a low absorption cross section. As a neutron is ejected from the uranium-235 in the fuel rod (or, in rare cases, dissolved in the coolant itself), the atoms with which it collides will either scatter or absorb the neutron. The chance of each event is expressed as a nuclear cross section, or effective area presented by the nucleus, and has the units barns (1 barn = 1× 10-28 m2).  The reason a high scattering and low absorption cross section is optimal is that the coolant should not eat the neutrons before they can be taken up by the fissile material. In the cases when coolant does absorb neutrons, however, the resulting radioactivity should have a short lifetime. Lastly, cost-effectiveness is a relevant consideration for reactors.
Note also the coolant affects significant aspects of the reactor itself, such as the operating temperature and pressure, the size of the core, and methods of fuel handling.
Since no coolant qualifies as perfect for all, various substances are used in industry. Below I will cover two common coolants: water and liquid sodium.
The two major types of water-cooled reactors are light water reactors (PWR) and boiling water reactors (BWR). Both use light (normal) water, but with slightly differing cooling mechanisms. In a BWR, the water turns into steam in the reactor core and is then pumped directly to the turbines that power electrical generators. In a PWR, the primary loop of coolant flowing through the core is at very high pressure (2250 psi) so it will remain a liquid.  It then transfers heat to a secondary loop of water that vaporizes and turns the turbines. This latter method ensures that any radioactivity activated in the coolant remains within the reactor. Because the heat of vaporization that is required for the phase change from liquid to steam limits thermal efficiency, there is currently research being done on a Generation IV supercritical reactor.  Light water is a good coolant for thermal reactors but not for fast breeders; pressurized water also moderates (slows down) the neutrons because hydrogen-1 (H-1), which comprises much of water, has a scattering cross section of σ = 82.03 barns, far larger than any other atom.  PWRs have an intrinsic failsafe should the reactor overheat to the point where the water in the primary loop boils; neutrons interact less with steam and do not get thermalized, so the abundance of fast neutrons causes the rate of fission to drop. After a few minutes, the reactor achieves passive shut-down.
An even more effective coolant and moderator is heavy water, or deuterium (liquid D2O), because its absorption cross section is three orders of magnitude smaller than that of hydrogen. However, it is also prohibitively expensive: approximately $2400/L. 
When it comes to fast breeder reactors, molten sodium is the coolant of choice because it causes negligible moderation. Not only one of the cheapest available metals (DuPont reactor grade Niapure is approximately $1.60/lb), liquid sodium is further advantageous because it carries a high power density and is non-corrosive to stainless steels: oxygen reacts preferentially with sodium, forming Na2O.  Like PWRs, the sodium-cooled fast reactor (SFR) utilizes a primary coolant loop that transfers heat via a steam generator to a separate water cycle. The sodium becomes intensely radioactive from contact with the fuel, but it stays contained within the reactor and has a short half-life of approximately 15 hours.  Like light water, liquid sodium is inherently safe in loss-of-flow scenarios; its large heat capacity and good thermal conductivity prevent significant temperature rises
However, liquid sodium has significant disadvantages as well: it ignites spontaneous upon contact with the air, and reacts violently with water. Besides burning, sodium exposed to the air produces aerosols that are highly toxic and can cause equipment damage to the surfaces onto which they are deposited.  An operational concern is that the opacity of the coolant makes fuel handling and monitoring more complicated.
An alternative to liquid metal is molten salt. This coolant can run at high temperatures for better thermodynamic efficiency, but remains at a low vapor pressure, which reduces the effects of mechanical stress and increases the intrinsic safety of the reactor. Since heat transfer by molten salt is so efficient, reactors can be designed with smaller cores and less complicated piping systems. Structurally, the biggest difference is that the fuel – a mixture of sodium, zirconium and uranium fluorides – can be dissolved into the coolant itself, a set-up that eliminates the need for fuel fabrication and the disadvantages of having variable isotopic ratios within the fuel rods. 
Other nuclear reactor currents include liquid lead, gases such as helium and carbon dioxide, and organic compounds.
|Table 1: Absorption and Scattering Cross Sections for Various Coolants and Fissile Materials.  Figures in parentheses are uncertainties|
© Suraya Omar. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 R. L. Murray, Nuclear Energy: an Introduction to the Concepts, Systems, and Applications of Nuclear Processes. (Butterworth-Heinemann, 2009).
 P. Gunter, "Safety Problems with Pressurized Water Reactors in the United States," Nuclear Information and Resource Service, March 1996. - This reference is volatile. NIRS is also a virulently anti-nuclear organization. - RBL
 "A Technology Roadmap for Generation IV Nuclear Energy Systems," Generation IV International Forum, GIF-002-00, December 2002. - GIF is a pro-nuclear lobbying organization. This is not a DOE document. - RBL
Neutron Scattering Lengths and Cross Sections. - This reference is volatile. - RBL
 Fisher Scientific. - This reference is volatile. The link is also to a promotional site. - RBL
 Sodium as a Fast Reactor Coolant, Argonne National Laboratory, 3May 2007. - Power Point presentations are not allowed as references. - RBL