Using Google's Ngram Viewer, here's the breakdown of Stata vs. SAS vs. SPSS.
Stata didn't do as well as I hoped, but in taking a closer look there are at least a couple of reasons to be optimistic about Stata's prospects.
(1) SAS is benefitting from lot's of books written about the British Special Air Service (SAS).
(2) As of yet, there doesn't appear to be a way to refine these searches with boolean search parameters. If so, we could have searched for "SAS -British" or "SPSS | PASW", etc.
(3) I couldn't find a way to search for the software 'R' using Ngram.
(4) Stata seems to have as much, if not more, web presence / resources as the other software packages.
Using a regular google search:
"Stata" + statistical software 22.3 million pages
"SPSS" + statistical software 28.2 million pages
"SAS" + statistical software 17.6 million pages
"PASW" + statistical software 53K pages
"R" + statistical software: 7.7 million pages
GoogleBattle.com has Stata ahead of SPSS by a count of 35 million to 13 million pages (besides leaving out the "statistical software" part, I'm not sure what else explains the difference)
(5) Finally, while more books are being published in modern times (especially with the increasing output of the Stata Press), this graph at least shows an uptick in Stata presence in Google Books since 1990:
Other fun Google NGram Viewer comparisons include:
Probit v. Logit (is that a CDF?)