Peter started off by pointing out that since Google hires Ph.D's in their regular developer positions they often end up treating their developers as researchers while treating their researchers as developers.
Google's goal is to organize the world's data. Google researchers aid in this goal by helping Google add more data sources to their search engines. They have grown from just searching HTML pages on the Web to searching video files and even desktop search. They are also pushing the envelop when it comes to improving user interfaces for searching such as with Google Maps.
Google Suggest which provides autocomplete for the Google search box was written by a Google developer (not a researcher) using his 20% time. The Google Personalized site allows users to edit a profile which is used to weight search results when displaying them to the user. The example he showed was searching for the term 'vector' and then moving the slider on the page to showing more personalized results. Since his profile showed an interest in programming, results related to vector classes in C++ and Java were re-sorted to the top of the search results. I've heard Robert Scoble mention that he'd like to see search engines open up APIs that allow users to tweak search parameters in this way. I'm sure he'd like to give this a whirl. Finally he showed Google Sets which was the first project to show up on the Google Labs site. I remember trying this out when it first showed up and thinking it was magic. The coolest thing to try out is to give it three movies starring the same and watch it fill out the rest.