Over the last year, VincentYu, gwern and others have provided many papers for the LessWrong community (87% success rate in 2012) through previous help desk threads. We originally intended to provide editing, research and general troubleshooting help, but article downloads are by far the most requested service.
If you're doing a LessWrong relevant project we want to help you. If you need help accessing a journal article or academic book chapter, we can get it for you. If you need some research or writing help, we can help there too.
Turnaround times for articles published in the last 20 years or so is usually less than a day. Older articles often take a couple days.
Please make new article requests in the comment section of this thread.
If you would like to help out with finding papers, please monitor this thread for requests. If you want to monitor via RSS like I do, many RSS readers will give you the comment feed if you give it the URL for this thread (or use this link directly).
If you have some special skills you want to volunteer, mention them in the comment section.
Document delivery services can provide scans. However, there probably aren't any legal services which'll scan entire books for you due to copyright law. I have a hard time getting different interlibrary loan departments to get me scans of some smaller documents as well, even if you can verify the documents are in the public domain.
The easiest thing in this case would be to use a good scanner in a library. I'm fond of the overhead ones.
I keep a list of certain rare books and articles that can be found in particular libraries, and go scan a bunch of them in batches when I have the opportunity. Yesterday I visited the Library of Congress and scanned a fair number of things which could not be found elsewhere.
Edit: I assumed above that gwern does not have a copy. Vaniver in reply to me gives a good option if gwern does have a copy.
I was thinking that if there were no digital editions yet, I could perhaps buy a used copy and either debind (for flat pages) & scan it myself or use one of the services like 1DollarScan. The problem with the latter is that I don't know how well it would work with a math book, and some of them won't return the debound pages to you...