The new version of the Google Android app has a new notification that can send you a notification when a new Google Doodle is on the Google home page. Often times, believe it or not, I do not see the Doodles because I rarely go to the Google home page directly. I subscribe to the Doodle RSS feed, that is how I spot most of them. But now, you can turn on a notification as Android Police reports.
Here are the settings:
Artem Russakovskii gave me the heads up on this....
Forum discussion at Google+.