Remember when you want to cool something down, the best way is to transfer that excess heat to another medium and then remove that medium. Water is very good at this for it is liquid between 32 and 212 degrees and thus flows. You can develop a simple pumping system to get the water to the heat source and then another pumping system to take the heated water AWAY from the heat source. AS long as the temperatures of the water is above 32 no problem (In the Three mile Island Nuclear incident in the 1970s, a vial stuck open, leaving all the water to escape, the reactor overheated before anyone caught on and turned the water back on).
As to the 32 degree problem, there are ways around that. First most rivers do NOT freeze from top to bottom. The reason for this is ice is lighter then water so it floats on top of the water and when the ice is solid, it acts as an insulation to the rest of the water. Another factor is most areas of the world (Actually all of the world) Ground temperature tends to be the same as the annual temperature. Outside of the extreme North and South that is above 32 degrees, thus if you move the water via pipes below the local freeze line (18-24 inches below the ground surface) the water in the pipe will NEVER freeze, no matter how cold it is above ground. Both of these known facts about water gives water an edge as a coolant even in areas of severe winters.
A further factor is water "will raise to its own level" if in a closed system like a pipe. This is why the water flows to your second floor bathroom, as long as the bathroom is below the intake of whatever is your water source. For most people their immediate water source is your local municipal water tank. Water is pumped into the tank, but then it flows into the municipal water system (Which is more or less sealed, leaks occur but most cases minor). This is true even if the water has to go down a hillside and then back up another to get to your home. As long as the water tank is above your home, the water will flow into your home as long as the pipeline is sealed (And most of the time it is, but when it is not, you quickly find out when you find the water no longer come out of the sink when you turn the handle). This characteristics of water has been known for millennia, even the Romans used it.
My point is simple, it is hard to beat water as a coolant, it takes a huge amount of heat to convert it to steam (and the amount is known and has been known since the early 1700s). It flows readily and thus can cool down most things by sheer volume of water passing over a heat source. If it gets to hot water becomes steam that goes into the air, leaving space in the liquid sections for more water (Which will be much colder then the water already next to the heat source).
In Chernobyl the problem was the safety systems had been turned off, including the one to provide extra water. What water remained in the system boiled into steam, which could NOT cool down the reactor (Steam can NOT cool things down, water can). Worse the design had a fatal flaw, as you powered DOWN the reactor could overheat do to an increase in reactor temperatures since
This steam later contributed to the reactor blowing up (Notice the lack of water at this point in the history of the disaster). The disaster itself took place over a period of Seconds, no way for water or any other method to cool down the reactor. The disaster had more to do with people NOT following safe operating procedures and a basic design that required strict following of procedures. Worse the control rods were made of two materials, the first part was light water so to cool the system down, and then as the rod continued into the core the core then the boron Carbide moderator material entered the reactor. The affect of this was to INCREASE reaction as the rod entered (The water part) then only as the part with the Boron Carbine entered the core would the reaction DROP. While one of the reason for this was to keep the system cool (i.e. the water) by making the rod out of TWO elements it did two things poorly. There was NOT enough water in the Rod to truly cool down the reactor as the rod was first entered into the core AND the Boron Carbide, which would slow down the reaction, was delayed by the water part of the rod as the rod as a whole was pushed into the core.
My point the water did its job of cooling the reactor in Chernobyl, the problem was the sudden increase in power caused by the type of rod used at Chernobyl. Nothing could have cooled down that reactor in the 3-5 seconds it took to over heat, an overheating caused by a sudden increase in nuclear reaction do to the design of the reactor.
My point is simple, water is generally the best coolant, it flows, boils away if overheated (And has a way to escaped, another problem of the Chernobyl disaster, the steam could NOT escape and be replaced by water) and is plentiful and cheap (in most of the world). It works at most temperatures people live in (And in those areas that water is frozen all or most of the year, you can still work around its problems but it is much more difficult thus it is rare to have nuclear plants in the Arctic Regions). Furthermore water flows, and thus can be directed to a source of heat quickly and be replaced by even more water if more is needed (and flow away from the hear source with the excess heat, thus taking the heat with it).
For more on Three Mile Island:
http://en.wikipedia.org/wiki/Three_Mile_Island_accidentFor more on Chernobyl
http://en.wikipedia.org/wiki/Chernobyl_disaster