Occam's Razor (also Ockham's Razor), is a principle attributed to the 14th century logician and Franciscan friar, William of Ockham that forms the basis of methodological reductionism. It is nowadays usually stated as follows:
The principle is most often expressed as Entia non sunt multiplicanda praeter necessitatem, or "Entities should not be multiplied beyond necessity", but this sentence was written by later authors and cannot be found in his surviving writings. William wrote the Latin Pluralitas non est ponenda sine neccesitate, which translate literally into English as "Plurality should not be posited without necessity".
Dave Beckett of the University of Kent at Canterbury writes: "The medieval rule of parsimony, or principle of economy, frequently used by Ockham came to be known as Ockham's razor."  (http://wotug.ukc.ac.uk/parallel/www/occam/occam-bio)
Occam's Razor has also been referred to as the "principle of parsimony" and the "principle of simplicity" and "K.I.S.S." (keep it simple, stupid). Another proverb expressing the idea that is often heard in medical schools is "When you hear hoofbeats, think horses, not zebras."
Occam's Razor has become a basic principle of the scientific method. It is important to note that it is a heuristic argument that does not necessarily give correct answers; it is a loose guide to the scientific hypothesis which contains the least possible number of unproven assumptions and is the most likely to be fruitful. Often, several hypotheses are equally "simple" and Occam's Razor does not express any preference in these cases.
For example, after a storm you notice that a tree has fallen. Based on the evidence of "a storm" and "a fallen tree" a reasonable hypothesis would be that "the storm blew down the tree" -- a hypothesis that requires only one assumption--that it was, in fact, a strong wind that knocked over the tree, rather than a meteor or an elephant. The hypothesis that "the tree was knocked over by marauding 200 meter tall space aliens" requires several additional assumptions (concerning the very existence of aliens, their ability and desire to travel interstellar distances and the alien biology that allows them to be 200 meters tall in terrestrial gravity) and is therefore less preferable.
Occam's Razor is not equivalent to the idea that "perfection is simplicity". Albert Einstein had this in mind when he wrote in 1933 that "The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience" often paraphrased as "Theories should be as simple as possible, but no simpler." It often does happen that the true explanation is much more complicated than the simplest explanation. Hence some people have restated Occam's Razor as "The simplest explanation is the best." (or is "the true one")
There are various papers in scholarly journals deriving versions of Occam's Razor from probability theory and applying it in statistical inference, and also of various criteria for penalizing complexity in statistical inference. Recent papers have suggested a connection between Occam's Razor and Kolmogorov complexity.
One of the problems with the original formulation of the principle is that it only applies to models with the same explanatory power (i.e. prefer the simpler one of equally good models). A more general form of Occam's Razor can be derived from Bayesian inference and Bayesian model comparison[?], which can be used to compare models that don't fit the data equally well (see e.g. Duda, Hart & Stork, 2001). These methods will optimally balance the complexity and the power of the model.
In the philosophy of religion Occam's Razor is sometimes used to defeat arguments for the existence of God and support the rationality of atheism. These applications of Occam's Razor are not considered definitive, since they often hinge on highly debatable notions of "simplicity". For example, postulating special creation involves some obvious big assumptions--but to claim that evolution is a "simpler" hypothesis requires that one quantify the exact nature and magnitude of the assumptions on which it rests.
William may have been inspired by earlier thinkers. For example, Book V of Aristotle's Physics has the statement "Nature operates in the shortest way possible."
Galileo Galilei notably lampooned Occam's Razor in his Dialogue. The principle is represented in the dialogue by Simplicio.