As in almost any endeavor there is the law of diminishing returns. At some point more fans will not help cool the parts under heat sinks. Here is some background, using plumbing as an analogy. Consider heat generators as pumps. Consider the interface between the pump and a heat sink as a certain size pipe. Considering it this way, if the pump increases speed (puts out more heat), the flow through the pipe increases up to a point where no more water (heat) can flow through that size of pipe (quality of heat sink interface). This is why there are after-market heat sink compounds overclockers use because they decrease the interface heat resistance (in plumbing terms, increase the size of the pipe).
The heat sink itself can be thought of as a plumbing pipe of a particular size. At some point it reaches saturation and cannot transfer any more heat out of it than heat is put into it. Blowing a fan on a heat sink helps, keeping the plumbing analogy going, as drain pipe connected to the heat sink. This is why when you blow harder on the heat sink, you can get more heat out of it. That said, at some point, more blowing will not get any more heat out because the heat sink itself has a limit to the speed it can transfer heat from the interface to the heat generator and it's fins.
Practically, a front case fan, a rear case fan, a side fan and top fan will be the maximum number of fans you can use before the laws of diminishing returns kicks in. In other words, one more fan will not help remove the heat from a heat sink that is already at it's limit in how fast it can transfer heat.
Adding a little more analogy that helps clarify things, consider a solid bar of copper. If you hold one end of it and apply a torch to the other end, you will notice that the end you hold does not get hot for some period of time. This because any metal has a thermal resistance. Complicating things is the fact that as the heat is applied to the one end of the bar, heat is not only traveling through the bar to the other end, but it is radiating into the air surrounding the bar. This gets me to the principle of fins. If you have fins attached to the bar, much of the heat will be radiated into the air through the fins and you would find it takes a lot longer for the end of the bar you are holding to get warm.
It is important to understand the limitations of a heat sink because microprocessors and graphics processors generate a lot of heat and as they work harder, the rate of heat they generate goes up. Not only is their a limit in how fast you can transfer heat through the interface (the heat sink compound on top of the chip between it and the heat sink), there is also a limit in how fast the heat can be removed from the heat sink. At some point the chip gets too hot and fails.
Now, some overclockers are using water blocks since water (keeping the plumbing analogy) is a bigger pipe (lower thermal resistance) than metal. In addition, since the water is being circulated, new cool water is constantly coming into the water block on top of the chip. There is still that pesky interface between the water block bottom face and the top of the chip itself. At some point, no matter how fast the water flows, the chip will overheat, assuming the chip is being overclocked.
I hope this information helps you understand why, at some point, adding more fans won't benefit you.