One of the principle arguments made by Intelligent Design Creationists (IDCs) is often referred to as "irreducible complexity" (IC), coined by Michael Behe of Lehigh University and the Discovery Institute's Center for Science and Culture. The argument is essentially that at the molecular level there are systems with multiple components that must all be present in order for the system to function. As Behe said in his book Darwin's Black Box,
An irreducibly complex system cannot be produced directly by numerous, successive, slight modifications of a precursor system, because any precursor to an irreducibly complex system that is missing a part is by definition nonfunctional
This argument, while being lauded by IDCs and their acolytes, has made barely a ripple in the scientific community. As far as I know, not a single one of Behe's fellow molecular biologists agrees with him, and the idea has been widely panned in the scientific literature. The two primary examples that Behe used are the bacterial flagellum and the blood clotting cascade. Both of those molecular system, he argued, are irreducibly complex - remove a single component from the system and the system doesn't work at all. His fellow molecular biologists have pointed out numerous flaws in his reasoning on these two systems, however.
Ken Miller, a cell biologist from Brown University, has hammered Behe's argument from the start, and for good reason. For example, in a chapter in a book coming out sometime this year, Miller points out that there are in fact functional precursors to the flagellum that could have been selected for, then later adapted to a new function. He writes:
The most powerful rebuttals to the flagellum story, however, have not come from direct attempts to answer the critics of evolution. Rather, they have emerged from the steady progress of scientific work on the genes and proteins associated with the flagellum and other cellular structures. Such studies have now established that the entire premise by which this molecular machine has been advanced as an argument against evolution is wrong the bacterial flagellum is not irreducibly complex. As we will see, the flagellum the supreme example of the power of this new "science of design" has failed its most basic scientific test. Remember the claim that "any precursor to an irreducibly complex system that is missing a part is by definition nonfunctional?" As the evidence has shown, nature is filled with examples of "precursors" to the flagellum that are indeed "missing a part," and yet are fully-functional...