Google's birthday has shifted around over the years, but it currently is celebrated on September 27th. The exact year of Google's "birth" depends on how you measure it.
In the summer of 1995, Google founders Larry Page and Sergey Brin first met at Stanford.
In January of 1996, the Google founders started working on a new search engine called BackRub.
This search engine used an innovative new approach to finding pages ranked by relevancy. The search engine was renamed Google, and the algorithm it employed was named PageRank.
The Web domain www.google.com was registered in 1997, but Google officially opened for business in September of 1988.
Generally, Google uses that 1998 date to calculate their age in years. By most accounts, the true day of the official Google opening was September 7th, but Google has shifted the date around, "depending on when people feel like having cake." [The link that originally contained that quote has since been moved or deleted by Google.] In recent years, people at Google feel like having cake on September 27th. Expect to see a Google doodle on that date. If you want to get an early sneak peak, try looking at Google in a country with an earlier time zone.