Google app on Android will let you disable Doodles in the home screen widget. If you don't like the little animation that shows up when you unlock your phone, or during special events in the year, you can turn it off. To disable the feature, head to the Labs testing section in the app and select "Search widget doodles." You can then turn the option off there.
Unfortunately, Google hasn't rolled the feature to everyone. You can check out if you have it by heading into the app and click on the More in the bottom right corner of the app. You can select Labs there. Labs is a way for Android users to play around with experimental Google app features. There are three available features: Search Weight Doodles, Pinch to zoom on search results, and Screenshot editing.
Source: Android Police