There are two, or even three aspects to the question, which we shall address in turn:
1) How many cubits tall was Goliath (a question of textual criticism)?
2) How long was a cubit (a question of archaeology)?
3) How reliable is the Bible's account (a question of theology)?
For the first question, the evidence is pretty straightforward: The Masoretic Text and the Vulgate, its Latin translation, pegs his height at "six cubits and a span," and the English translations of Josephus and 4QSamA, along with those of many manuscripts of the Greek Septuagint, read "four cubits and a span." There are even a couple of Greek manuscripts that read "five cubits and a span." Clearly, there was some tampering with the text. I found the following chart online, which I edited slightly but can't vouch for its accuracy (it matches information given by Clyde Billington and J. D. Hays):
What we should note from this difference is that throughout the history of Christendom, children getting a religious education got two very different ideas of Goliath's height. Were they Orthodox, they probably visualized Goliath as being very tall, but not particularly gigantic: between 6' 9" and 8 feet tall. Were they Jews or Catholics, however, they all envisioned him as being somewhere between 9'9" and 11 feet tall. The problem with this latter height, however, is that it exceeds the height of anyone known to science, and would physically result in a monstrosity too encumbered with his own weight to be of any good in battle.
But this objection begs the question of the length of a cubit--the second question. A cubit, we know, is the distance from the tip of the middle finger to the bend of the elbow. A person is typically 3½ of his own cubits tall (the White Man is 3.57 of his cubits tall). So for Goliath to be even 4½ cubits tall, we would have to be speaking of an objective measurement, outside of his own body. Define the length of this measurement, and only then we can decide whether Goliath was merely tall, or a true giant--regardless of the text followed.
Well, the standard modern definition of the cubit is 18 inches, resulting in standard height of 5 feet 3 inches. But we are not interested in the modern length of the cubit, but the ancient one. And for that, several different lengths have been determined, anywhere from 445 (17½") to 610 mm (24"), with a most likely length of about 524 mm (20.6 "). Note that the NIV's definition of a cubit, based on conversion figures given in the footnotes, has ranged from 18 to 21.65 inches. Taking a most likely range of 20.5 to 21.5 inches, the two texts would give Goliath a height of 92.25" to 96.75" and 133.25 to 139.75 inches respectively; in other words, he was either about 8 feet tall, or about 11½ feet tall. The first is at the upper range of what is attainable through genetics and diet; the second is physically impossible for homo sapiens, as witnessed by anyone with a giantism disorder continually growing until dying from complications of their extreme size before attaining anything over about 9 feet in height.
As for the third question, Bible commentators have traditionally accepted the larger size for Goliath, especially as it is even smaller than the reported height of Og of Bashan and other figures from ancient history. They quote from Herodotus, Diodorus Siculus, and Pliny:
"The tallest man that hath been seen in our days was one name Gabara, who, in the days of Claudius, the late Emperor, was brought out of Arabia: he was [over 6½ cubits] tall."
as well as Josephus:
"A Jew, named Eleazar, whom Vitellius sent to Rome, was seven cubits high."
But again, this begs the question of "how long is a cubit?" Let's look at the mention in the book of Deuteronomy, which contains this interesting note on "the last of the Rephaim:"
"For only Og king of Bashan remained of the remnant of giants; behold, his bedstead was a bedstead of iron; is it not in Rabbah of the children of Ammon? nine cubits was the length thereof, and four cubits the breadth of it, after the cubit of a man."
So, Og was specifically called a giant (Repha)--a word not used in 1 Samuel, as he was the last of the race. Because of this qualification, Hebrew mythology states that Og was one of the Nephilim who rode out the Flood clinging to the back of the Ark. How else could they account for his enormous size? But note the qualification to his size: it was measured in "the cubit of a man." And we still don't know exactly how long that was.
Here's an idea. Let's assume that the Pyramids of Egypt were an exact number of cubits wide at the base, and see if that gets us a standard to work with. It turns out that the dimensions of the Egyptian Royal Cubit, already known, are an exact fit for the Great Pyramid: 440 cubits wide, 280 cubits high (each stone layer then being one and a third cubits high), and 356 cubits deep. The ridge length even comes out to the quarter-cubit, and the inclination is 5½ palms per cubit. The cubit in question? 52.4 cm or 20.6 inches. With a cubit that size, anyone over six of them in height is going to be a monster; but anyone four and a half of those cubits high is what normal-sized people would call a giant. So we're stuck with a really huge bed for King Og--but left with no specific measurements of the giant himself, leaving the jury still out on whether or not humans really could grow to fantastic size back in ancient times.
One further biblical reference must be mentioned: 1 Chronicles 11:23, which refers to a five-cubit tall Egyptian warrior. If Goliath was half a cubit shorter, then it's no wonder he is never directly referred to as a 'giant', because as giants go, he would have been less than average height. So is it any surprise that he volunteered as the Philistines' champion? Shorter soldiers (and basketball players) are known for being bolder and more aggressive, as if to make up in courage for what they lack in height. If 4QSam(a) is right, Goliath was a short tall man.
So, how tall was Goliath--was he a human giant, or a genetic monstrosity? I'm going to go with the 4½ cubit measurement and say that he was just a giant. Here are my reasons:
1. The Egyptian Royal Cubit puts his height at the upper range for a healthy human, but only if we read the Hebrew number as a daleth rather than a waw (the difference is that the larger number has a side-stroke that is a bit shorter than the smaller number).
2. While it is possible, even probable, that the Rephaim were genetically capable of reaching superhuman heights, Goliath is never directly referred to as a 'giant' (Repha or Gibbor). Instead he is connected with 'the sons of the Rapha of Gath' (a slightly different spelling in the Masoretic Text), apparently a rather tall race of Philistines. He and his four 'brothers' were huge, as evidenced by the size of their armour, but not gigantic.
3. It is apparent that humans in general were taller directly after the time of the Flood (The Egyptian Royal Cubit yields a standard height of six feet tall), but as the natural cubit shrank, followed by the standard cubit ('the cubit of a man'), Goliath's height of 4½ cubits was no longer commensurate with the size of his armour. People retained knowledge of a then-extinct race of giants, and assumed them to be taller than they really were--but definitely taller than the 6½ feet that Goliath's height now yielded. Thus the shortened stroke of the numeral, yielding a taller height for the giant, became accepted in the continued transmission of the Hebrew text--from whence it found its way into all later translations thereof.
A couple of postscripts:
1. Adam Clarke mentions a man of the name of John Middleton, born at Hale, near Warrington, in Lancashire, in the reign of James the First, who was more than nine feet high. "Dr. Plott, in his history of Staffordshire, says, that `his hand, from the carpus to the end of the middle finger, was seventeen inches, his palms eight inches and a half broad, and his whole height was nine feet three inches; wanting but six inches of the height of Goliath of Gath.'"
Indeed this is the height listed on The Childe of Hale's tombstone, but I'm still waiting on confirmation of the actual size of his burial plot. The descriptions of his physical prowess better fit someone of about eight feet in height (feet and inches not having been yet effectively standardised at his death).
2. It was common in ancient Egyptian artwork to picture royalty as much taller than the common people, or even of their own royal sister-wives. But even among royalty, there is a possibility that some were depicted as being truly taller than others; this picture, for instance:
Note the comparison in heights between the figures to the leftmost and rightmost of the picture. Note also that the tallest two figures are dressed differently than all the others, and have been subsequently defaced (along with both of the animals).
Like I said, this is a hot topic in Biblical research lately. I'm already compiling information for another post that will look at the textual question more closely.
UPDATE AUGUST 2014
This article makes two claims, the first unsubstantiated:
1. The Hebrew cubit was shorter than the Egyptian cubit.
2. A special race of giants could genetically be capable of attaining a 13-foot height and weight of 1500 pounds.