The special logos appearing on Google home page is called Google Doodles. Google used to do various modifications to its logo such as birthday of famous people, holiday logos, major events and etc. As of today Google created around 950 doodles. Even Google made interactive doodle such as Pac-Man logo. Here are some popular Google Doodles to check out.
Check out this Pac-Man logo, You can go here and play Pac-Man on Google doodle.