Why upload to academic preprint sites like arXiv? The recent question about the legality of uploading to arXiv made me realize that I don't have any understanding of why one would upload to a preprint site.  (I don't work in a field where they seem to be common.)

Why would one be concerned about getting a manuscript on arXiv, if it's already under review with a journal? 

Is it because of the long publishing timeline of journals?  (That could explain why computer science &mdash; which publishes much more in conferences &mdash; doesn't seem to do much with them.)
In mathematics, there are several reasons to post to the arXiv:


It provides free access to papers that might otherwise be hidden behind paywalls.  Of course you could achieve this by posting on your web page, but your web page may move or disappear, while the arXiv is far more stable.  This means it's better for archival purposes and it's better suited for citations.  [Note that this is not just about preprints: it continues to be relevant long after publication.]
It attracts readers.  Many people pay close attention to arXiv postings in their area, in a way that doesn't happen as much with journal tables of contents.  I don't have statistics, but my impression is that a substantial fraction of the people who learn about my papers do so through the arXiv.  If you can get noticeably more attention for your research with almost no additional effort, why wouldn't you?
It establishes priority.  Submitting to a journal does not: if you submit to a journal without circulating your work publicly, then you may still end up sharing credit with anyone who makes the same discovery before your paper is made public.  The way to establish priority is to distribute your work so widely that any competitors cannot credibly claim to have been unaware of it.  Submitting to the arXiv is the easiest way to show that you have done so: it's widely read, and it preserves all versions of the article with time stamps.
It's conventional.  This varies somewhat between subfields, but once arXiv use reaches critical mass in a given area, it becomes the standard way of announcing to the world that you have completed a paper.  At that point, not posting to the arXiv looks strange.


Compared with other fields, mathematics and physics are anomalous in making heavy use of the arXiv, with physics even more so than mathematics.  As I understand it, in high energy particle physics the arXiv replaced an elaborate system of paper preprint distribution that was used in the late 80's (and it rapidly became popular since it was obviously better than the paper infrastructure).  Usage spread to other areas of physics, from physics to adjacent areas of mathematics, and then further into mathematics.

Things are trickier in other fields, because many of the advantages depend on network effects.  If nobody in your field pays attention to a server, it's not conventional, and it counts for little or nothing regarding priority, then there's less reason to post to it (although it still has some value).  I'm not surprised that it catches on only slowly and spreads primarily to adjacent fields, but I expect green open access servers like the arXiv will become more popular over time.