Google has used 5 different favicons.
Google's 4th favicon was introduced in August 2012. The new simple blue icon looks similar to their 2nd favicon used prior to 2009. It also looks similar to the icon used in their mobile search apps and matches the color used in Android.
The colorful third favicon was introduced in January 2009, as the result of a contest which was won by André Resende. It was used until August 2012.
Google's 5th and current favicon was introduced alongside the new Google logo in September 2015. The icon integrates the four colors of the full logo.