The first Thrun vehicle I rode in was the Volkwagon Toureg (though not the original "Stanley"). This was not long after he won the 2005 Darpa Challenge and competed in the later 2007 version and had just moved to Google. We had a fair bit of real world Lidar tracking data (from a very different space) and being just around the corner from the Google shop and us having some industry notoriety he knew about us. He drove it over to talk with us, share info and give us rides. Later it was always one of their many Prius that I was around. I personally know a number of people involved in the project.
I have no idea currently their mix of vehicles, but the research was dominated by the Prius platform for many years.