God of the gaps
“”Explanations exist; they have existed for all time; there is always a well-known solution to every human problem — neat, plausible, and wrong.
“”No one infers a god from the simple, from the known, from what is understood, but from the complex, the unknown, and the incomprehensible. Our ignorance is God; what we know is science.
|—Robert Green Ingersoll|
The "god of the gaps" is theological reasoning which invokes divine intervention as a way to understand natural phenomena that science is presently unable to explain: Since we don't know how x happens, it is assumed that Goddidit. Of course, scientists and most rationalists would argue that naturalistic explanations for still-mysterious phenomena are always possible.
The god of the gaps is one way for intelligent and scientifically literate theists to deal with the cognitive dissonance of believing in a transcendent god.
"God of the gaps" is a bad argument not only on logical grounds, but on empirical grounds: there is a long history of "gaps" being filled and the gap for God thus getting smaller and smaller, suggesting "we don't know yet" as an alternative that works better in practice.
 History of 'gaps'
The human brain appears to be hardwired to find causes for any "effect" experienced in the world, from eerie sounds, to scary thunder, to terrifying ground shakes, and deadly diseases. Early humans, just beginning to seek explanations for natural things they experienced in their world found answers by saying those things were caused by gods, or other supernatural figures (like ghosts or witches); many early "gods" are storm gods (such as Thor) or gods of the wind (the Kami, in Japan). The very act of birth was apparently seen as magical and godlike.
But as humans explored more, they found naturalistic answers to simple things they once attributed to gods. As humans developed a simplified scientific method, more "gaps" were filled with naturalistic answers. God or the supernatural were no longer needed as an explanation. And finally, as science took hold of humanity's quest to understand the world, each advance in scientific knowledge reduced the area where a divine power was necessary. Galileo and Newton undid the idea that planetary motion was accomplished through the efforts of angels. Lightning was revealed to be an electrical buildup and discharge in the atmosphere. We learned that earthquakes were shifts in the plates of the Earth's crust. Even things not yet proven can be shown to have likely or possible natural causes. For example, the discovery by astronomers of organic molecules in space revealed that life on earth had a possible explanation that did not involve a creator god.
 When 'gaps' are filled
When each gap is filled, the believer is forced to jump to the next gap. This game can continue ad nauseam, since human knowledge will never be able to explain everything (by definition of infinity, and by principles such as Gödel's incompleteness theorems). However, the argument is an instance of the logical fallacy of argument from ignorance. The ultimate "gap" that likely cannot be bridged is "well, god started everything", because even if something like the m-theory explaining how our universe could have "big banged" in the first place was proven to be true someone could always ask, "yes, but what created the membranes?".
 Life and evolution
One of the more prominent examples of current "God of the Gaps" thinking is the Intelligent Design movement, which claims that some aspects of how life formed are impossible to explain — not only with today's scientific knowledge, but ever.
Another well-worn God-gap is that of abiogenesis. Again, as there is no generally accepted explanation for the appearance of life on the planet, the position that Goddidit is taken as default by creationists.
The God of the Gaps argument finds what is perhaps its most popular manifestation in ideas about first cause. Ultimately, some people will always believe that something cannot come from nothing, and that any scientifically explained manifestation/creation of our universe will require that something "caused" it to exist. (There is, of course, rarely a serious question of what caused the causer.)
Amusingly, Gödel's incompleteness theorems prove that God will always have a little gap left to hide in, no matter how much humanity learns, but if God is used to fill that gap, there must be an inconsistency.
 The O'Reilly Paradox
Because many of the people using this tactic are fundies they often have a loose understanding of modern science. This produces an interesting phenomenon where the person trying to discredit science refers to a scientific principle that is well understood. A famous example of this is Bill O'Reilly's declaration that ocean tides were an unexplained phenomenon, implying the Almighty willed the oceans to move. This error is hilarious, as the cause of tidal movement is well understood. Another less famous, but still incredibly hilarious example comes from one of SpiritScience's videos. Here we see a mixture of falsehoods and facts that could easily be explained by a ten second Google search, such as capillary action or surface tension.
 See also