Pascal's Wager
Fallacious argument trotted out by religious believers, particularly in the Judeo-Christian tradition, in favour of belief in divinity.  The argument goes as follows: you may either believe in God or not, and he may or may not actually exist.  If you believe in him, it is irrelevant if he doesn't exist (and by extension there is no afterlife), while if he does you are offered a place in the light eternal.  If you don't believe in him, then if you are right it is irrelevant to your metaphysical fate and if you are wrong you will go to Hell.  Therefore you might as well believe in him ... what do you have to lose?

Leaving aside the pettiness the argument ascribes to a supposedly all-loving and all-powerful God who has supposedly gifted us with some of the finest intellects on the planet, the problem with the argument is that it ignores the fact that a life lived in the firm belief in a supernatural entity is likely to be different from one lived in the acceptance that there is no such being.  Belief in God seldom comes on its own, but as part of the package offered by a formal religion.  As such, it frequently involves the acceptance of taboos and fears that have nothing to do with the rational or the physical world, and that are liable to crush any hope that many people may have for happiness it what may well be the only life they will ever know.  Arguably it is shameful to give over what are likely the finest minds to have evolved in billions of years of life on Earth to such malarkey.  Furthermore, there is of course the small matter expounded by that great religious thinker, Homer J. Simpson, in the well-known Simpson Rebuttal.
Pascal's Wager is a fallacious wager.