Prof. Ripley today announced on the r-devel mailing list that CRAN now has it's 5000th R package:
Package 'quint' brought the number of packages on CRAN (for all platforms: some are Windows-only or non-Windows only) to 5000 a few minutes ago: see http://cran.r-project.org/web/packages/index.html.
That's quite a milestone! The number of CRAN packages has been increasing rapidly recently, as the chart below from The Popularity of Data Analysis Software shows. There were about 4200 pacakges available when R 2.15.2 was released on October 26, 2012.
And that doesn't count all the R packages available that aren't on CRAN. As of today, there are 749 additional packages in the Bioconductor repository, and hundreds more R packages on GitHub. (Anyone know how to get a count of R packages on GitHub?)
In any case, there are easily more than 6000 open-source R packages available. Kudos to all the developers who have contributed packages, and a special thanks to the tireless volunteers (especially Prof. Ripley) who manage the CRAN network, maintain its systems, and respond to CRAN submissions for approval. It's a great community service, and a huge part of why R is so successful.