By year: 2004, 14 citations. 2005, 22 citations. 2006, 69 citations. 2007, 43 citations. Note that the high number of citations in 2006 resulted in part from the publication of papers from conferences about law blogs, and that the number of citations for 2007 will likely increase in the future because not all journals have posted their final 2007 issues to the database. (Methodology: JLR database queries for “volokh conspiracy” limited to each year.)
UPDATE: Eugene, commenter Larry the Librarian, and David Zaring all point out that my methodology may undercount cites slightly for various reasons.