It was not until August 1999 that Catull was used for the Google logo we see today. Before it and the doodles, there was a Garamond-ish font with an exclamation point at the end similar to Yahoo!. The color sequence in the letters was however already shown.
Google officially launched a new logo design on May 6, 2010 that still uses the Catull font. Its shading style is however different, along with a more subtle shadow.
Google through the years.
Click image to enlarge.
You can also mimic the Google logo, colors included, using a free Google logo generator such as this. You simply type in a phrase and click Create, after which the tool will convert capital letters to small caps and randomly select a color for each letter. The resulting downloadable logo image is in GIF format.