James already gave a good overview... however I feel his treatment of the "Global Flood" interpretation is rather biased.
First off, almost no one proposes a "literal" reading of Genesis. The authors use occasional metaphors and hyperboles which are clearly not meant to be taken literally. That said, there are conjectures that phrases such as "spread out the heavens like a curtain" (Isaiah 40:22) are less metaphorical than we might know, but that's somewhat beside the point.
Why believe in a global Flood?
The Book of Genesis records:
|19 And the waters prevailed so mightily on the earth that all the high mountains under the whole heaven were covered. 20 The waters prevailed above the mountains, covering them fifteen cubits deep. 21 And all flesh died that moved on the earth, birds, livestock, beasts, all swarming creatures that swarm on the earth, and all mankind. 22 Everything on the dry land in whose nostrils was the breath of life died.
The thing about metaphors and hyperbole is they're usually easy to recognize. The above passage does not appear to be either; there's little material for a potential metaphor, and hyperbole is rarely specified with precise measurements. The often proposed reading of such passages is referred to as "historic" or "plain reading"; that is, how would someone approaching the text with no preconceived notions as to its interpretation be likely to interpret it?
What about some of the objections to this interpretation?
there does not exist enough water in any form (including ice) to cover the continents and mountain tops
This presupposes that the Earth today looks like the Earth prior to the Flood. In fact, all modern global Flood models are based on substantial topological changes coinciding with the Flood. A "flat" earth (that is, a hypothetical Earth which is a perfect oblate spheroid with no topological features) would actually be entirely covered by a more than two kilometers of water. The Bible tells us that the highest points were covered by a measly (in comparison) 15 cubits. (Further discussion of this, or other, points is encouraged to take place via additional Questions.)
most mainstream scientists state that there is no geological evidence for a global flood
Most mainstream scientists also assert that God doesn't exist, or if He does, He certainly had no involvement in the origins of stars, animals or people (in direct contradiction to Genesis 1). When looking at "scientific" evidence, it's important to consider whether that evidence has been interpreted through a world view that affirms God's Word, or one that has denied God a priori. In fact, when viewed from the starting point of God's Word, there is significant evidence of a global Flood, which James already cited.
mainstream scientists will generally dispute and critique [...] interpretations of the geological record [which would suggest a global Flood]. This can often lead to some allegations of great conspiracies and cover-ups by mainstream scientists.
Naturally, scientists whose a priori commitment is to denying God will seek to deny such claims. Mainstream "science" also claims that humans somehow came about through chance processes which ultimately started from nothing but non-living matter. This is despite that abiogenesis has never been observed or even shown to be plausible, nor has the ability of existing organisms to exhibit unbounded change ever been observed or shown to be plausible. (Conversely, we repeatedly observe the opposite of both points, as predicted by a plain reading of Genesis.)
Only crazies believe this... right?
The idea of "great conspiracies and cover-ups" is something of an exaggeration that misses the true problem, which has been predicted since at least the first century A.D.:
|2 Peter 3:3-6
|... scoffers will come in the last days with scoffing, following their own sinful desires. 4 They will say, “Where is the promise of his coming? For ever since the fathers fell asleep, all things are continuing as they were from the beginning of creation.” 5 For they deliberately overlook this fact, that the heavens existed long ago, and the earth was formed out of water and through water by the word of God, 6 and that by means of these the world that then existed was deluged with water and perished.
Interestingly, this not only predicts denial of Biblical history, but of the (global) Flood specifically. This is an important point, of course, with respect to the cited concerns of NT references and Biblical Inerrancy.
The critical point, again, is that the majority of people that reject a global Flood (or divine Creation, or Christianity in general) aren't doing so based on the evidence, but rather on the basis of a presupposition that God does not exist. Once God has been excluded, one can concoct various explanations to explain what is seen without invoking God. Such explanations are not, however, necessarily rational.
The book "I Don't Have Enough Faith to Be an Atheist" by Norman Geisler and Frank Turek gives an excellent overview of the flaws in the materialist worldview, along with some of the absurd things that materialism believes. It's a good starting point for understanding that the beliefs of materialism aren't based on evidence, but on an a priori philosophy. Many other resources go into much more depth with respect to specific beliefs, but understanding that the root of the problem is a desire to deny God (since we otherwise might be accountable for our actions), or to shape God's Word according to our own sinful desires (which otherwise might tell us we ought to not do the things that we want to do), will provide much better insight into how and why so many people hold views that are contrary to a plain reading of the Bible.
The problem is not "great conspiracies and cover-ups". The problem is not that the evidence points away from God (Romans 1:20 tells us quite clearly that the opposite is the case). The problem (as well described and predicted by the Bible itself) is human nature; as noted, most people don't want God to exist, so they start by choosing to exclude God and then make up stories to justify that belief. Humans are remarkably good at this sort of thing (just try talking to anyone that believes the Earth isn't mostly-spherical), and in areas not related to theology or origins debates, this is well established psychology. Thus, ask yourself; if we know this to be true of human nature in other areas, why should we believe it isn't also the case when it comes to belief in God, Creation, or the Flood? Only God's Word is a sure source of Truth.
What about specific denominational positions?
How, for example, do the major churches (Catholic, Orthodox, Baptist, Lutheran, etc.) interpret this story — is there an official teaching?
In my experience, beliefs can vary significantly within a denomination, or even within a particular church. There are, however, organizations (often pan-denominational) which are devoted to particular views.
For example, Answers in Genesis is so thoroughly committed to a historic reading of Genesis 1-11 that this is not only reflected in their very name, but they have built a 1:1 scale replica of Noah's ark as a combination museum and practical demonstration. Creation Ministries International states that "the great Flood of Genesis was an actual historic event, worldwide (global) in its extent and effect".
Conversely, there are organizations such as BioLogos (an organization dedicated to denying Special Creation as described in Genesis 1), which makes an equally clear statement: "there has never been a global flood that covered the entire earth, nor do all modern animals and humans descend from the passengers of a single vessel".