Before transferring to the Kindle, it might be worth tidying up the text file to make it more readable. This is especially easy using the command line in Linux -- I use the 'fmt' command to remove excess whitespace and line-breaks, and 'tr -d' to delete any annoying characters (in my case, asterisks) that one's browser saw fit to scatter throughout the saved text file. This is all taken care of by the single line:
cat oldfile.txt | tr -d \* | fmt -u -w 999 > newfile.txt
Update: a few further notes...
(1) Acrobat Reader is sometimes able to "save as text" even scanned-image PDFs. (I guess these must be "image+text" marked-up PDFs, rather than raw scanned images. But they look the same to the naked eye.)
(2) The method listed for JSTOR articles won't work for two-column scans (e.g. of books). Linux script 'unpnup' enables one to convert such files to single-column PDFs however. PaperCrop is a more powerful solution that works easily in Windows.
(3) Sometimes a book scan is of such bad quality that OCR just can't interpret it. In this case, one can use PDFread to cut up the images into kindle-sized bites, and assemble the images directly into a .prc or .mobi (Kindle-readable) file. This way one can read the scanned images themselves on one's Kindle, without them being shrunk to an illegible size. I've found that this works extremely well.