The Social Science Research Network (SSRN) has had over 37.4 million downloads.
Here's an excerpt from the announcement:
2010 is our 16th year and it is off to a great start. Our eLibrary (http://ssrn.com/search) has delivered over 37.4 million downloads to date and grown to 290,000 documents and 138,000 authors—increases over the last year of 53,000 and 22,000 respectively. Our CiteReader technology, developed with ITX Corp, has captured over 6 million references, 5.7 million footnotes, and close to 3.9 million citation links.