Certainly Google does not make such data public, though I'm sure that
they record it. The closest that you can get is the Google Zeitgeist,
which lists the top ten searches of the previous day/month/etc.
Google, and all other search engines as far as I know, regard data
about what its customers are searching for as very private. In the
original paper by Brin and Page, they say in section 1.3.2:
"Another important design goal was to build systems that reasonable
numbers of people can actually use. Usage was important to us because
we think some of the most interesting research will involve leveraging
the vast amount of usage data that is available from modern web
systems. For example, there are many tens of millions of searches
performed every day. However, it is very difficult to get this data,
mainly because it is considered commercially valuable."
This quote makes it seem unlikely that they would turn around and
publish the data.
After a brief search, I found this webpage, which might help you out.
http://www.dwoz.com/default.asp?Pr=59