
Literarily -- that is to say, without evaluating any given claim about the authenticity or truth of the contents -- the Qur'an is a collection of revelations of God given to Muhammad. From start to finish, it is first-person narrative. There is little like the stories of the Hebrew Bible or its law codes, and nothing like the gospels or letters of the New Testament. The closest parallel to the Qur'an's genre is the prophetic literature of the Hebrew Bible.
The collection is gathered into 114 suras (chapters), which are then arranged roughly in descending order according to size -- although the arrangement is not perfectly ordered in this way, the longer suras are in the beginning, the shorter ones at the end. The longer suras are really collections of revelations. We can actually see the breaks between revelations as the topic shifts dramatically. The exact reason that particular revelations were gathered into a single sura is usually unclear. At times it seems that the reason has to do with a key word that happens in two or more revelations.
Thus, the Qur'an is not a text that people approach in narrative fashion, starting at the beginning and proceeding in a line to the end. One can find words on, say, the final judgment in several suras, spread out through the Qur'an (???). In practice, the Qur'an is more like hypertext. Throughout its history, individuals have assumed the challenge of memorizing the complete Qur'an, and these individuals then have full access to all parts of the Qur'an based on allusion or theme. Indeed, its very name (which means, "the Recitation"), points both to its origin as spoken words to Muhammad, and to its primary way of being experienced -- not as a text to read, but as an oral experience, an associative experience (in which this hearing associates with that one, regardless of their "order" in a canon) rather than a linear experience (with a predefined start and finish). Furthermore, the "recitation" of the Qur'an is more accurately called "intonation". The text is almost sung, read according to a musical system that may vary from place to place. The result is indeed haunting and mystical, and traditional Islam maintains that many have been converted to Islam through the hearing of the recitations, even though they did not know Arabic.
The Qur'an is, of course, written in Arabic, the language of Muhammad. Islam has insisted since its beginning that the Qur'an is only the original text -- no translation is the equivalent of the Qur'an. Thus, Muslims worldwide study Arabic as a second language, and in time Arabic has become the dominant language of many non-Arabic Muslim countries. On the other hand, if the Qur'an required the spread of Arabic as a language, it alos cemented Arabic's development. Unlike English, which has changed dramatically over time (compare Beowulf with John Grisham's prose), modern Arabic is largely Quranic Arabic with additional vocabulary.
When Muhammad first reported the revelations to those around him, the Qur'an (the word referring to the revelation, not yet a book per se) was understood as the Arabian experience that paralleled the Israelite experience and later the Christian experience. In other words, the Qur'an was thought of as the revelation for the Arabians. But after Muhammad's death and the spread of Islam under the caliphs, the Qur'an came to be perceived as the final, perfect revelation in a series. The previous revelations -- Jewish, Christian, Sabean -- came to be seen as corruptions of the same revelation, and therefore inferior. Thus, the Qur'an makes refence to the biblical stories, but with corrections. For example, the son that Abraham nearly sacrificed was Ishmael, not Isaac. Because these "corrections" contradict the Qur'an's own picture of separate but equal revelations, critics might argue that the "corrections" came out of the community after Muhammad's death, but traditional Muslims do not believe that such changes to Muhammad's original message would be possible.