Can someone explain the basics of Kaluza-Klein Theory (with as minimal math as possible) and why it was discredited? Most of what I know about Kaluza-Klein Theory comes from a book I read a while back by Brian Greene called "The Elegant Universe". What he said was that Kaluza had figured out a way to incorporate a fifth dimension of space-time to the equations of relativity and out popped electromagnetism. Although he wasn't really specific, I was enthralled by this idea and figured that it must be the key to the Unified Field Theory (until I realized it was discredited).
Can someone explain this theory in greater detail and why it failed?
(I am not an expert in math, so preferably words over numbers, unless absolutely necessary)
 A: It is not really discredited, 

It is considered to be an important precursor to string theory.

It was attractive in uniting electromagnetism with gravity, but could not accommodate the weak and strong interactions. The standard model of physics developed and the  two could not be reconciled (that is the discredited part) until string theories with many more extra dimensions came along.

In the 1970s, as physicists began to realize that string theory contained extra dimensions, the original Kaluza-Klein theory served as an example from the past. Physicists once again curled up the extra dimensions, as Klein had done, so they were essentially undetectable (I explain this in more detail in topic 10). Such theories are called Kaluza-Klein theories.

A: You need to be careful to define exactly what you mean by Kaluza-Klein theory. Originally it was the theory developed by Theodore Kaluza in 1919, and subsequently further developed by Oscar Klein, however the term has come to mean any theory involving compactified extra dimensions. In this latter sense it is most certainly not discredited because the idea is widely used in modern theoretical physics.
The original KK theory wasn't so much discredited as abandoned because it didn't seem to be leading anywhere. Quantum mechanics had come along to describe electromagnetism and it wasn't clear how the KK theory fitted into this. Furthermore it wasn't obvious what mechanism controlled the compactification of the extra dimension i.e. what caused it to remain tightly rolled up rather than expanding to a size where it could be observed.
A: Kaluza-Klein theory is too mathematical to give much more than a superficial account here.
It adds an extra "electromagnetic" space dimension to Einstein's four-dimensional spacetime. The equations for General Relativity and electromagnetism turn out to have a surprising amount in common. By incorporating that extra dimension into general relativity, Kaluza and Klein found that the equations for electromagnetism also appeared.
The oddity was that the fifth dimension had to be very small. They speculated that it was closed and finite, a tiny ring like the cross-section of a hosepipe. Nowadays we say that it is "compactified". However two problems emerged.
One was that the theory also produced a scalar field (one with magnitude but no direction, like mass), but nobody can detect any experimental signs of its existence.
The other was that, as quantum physics developed, other forces besides gravity and electromagnetism appeared; the strong and weak nuclear forces. The latter three were explained at the quantum level by quantum field theory (QFT), leaving only gravity to be incorporated. For a long time people regarded Kaluza-Klein as discredited and sought to extend QFT instead.
But the search for a gravitational QFT theory led nowhere, so eventually some people went back to the Kaluza-Klein idea and began to add more compactified dimensions to accommodate these new forces. This led to the development of modern string theories, in which there are typically six such extra dimensions, making ten in all. (I say "theories" in the plural because the main contenders all turn out to be aspects of a unifying 11-dimensional M-theory).
But there are so many possible string theories that as a predictive model it is next to useless; whatever you discover in the lab, there will be a string theory somewhere that fits it, it explains nothing. Save for one thing. All string theories assume something called supersymmetry; there are twice as many fundamental particles as we currently have. However most versions of supersymmetry fall at the same hurdle as Kaluza-Klein; they predict such "sparticles" at energies where we have found no trace of them. So it is once again discredited in the eyes of half the physics community; the other half live in hope of building more powerful accelerators or drawing out a testable prediction.
