(written from a Production point of view)
Google Doodle of September 7, 2012 is an interactive homage by the search engine Google to the importance of Star Trek in popular culture. Made for the show's 46th anniversary, it was designed by Ryan Germick of Google.  It shows three scenes from The Original Series with letters representing the various characters.
The first scene shows Spock, Uhura, Kirk, Bones, Sulu, and a redshirt as the letters G, o, o, g, l and e respectively. The next scene has Kirk and the redshirt in the transporter room, with a cameo by tribbles. The final interaction has a Gorn appearing. Kirk then proceeds to fight the Gorn (the solution is the same "makeshift cannon" as seen in "Arena") and the redshirt "dies." Afterwards, Kirk and the burned redshirt appear back on the bridge. At the end, the USS Enterprise warps past, spelling out "Google" in the same font as The Original Series.
The 2012 New Years' Eve Google Doodle, which showcases Doodles for the year, had the Enterprise on a screen which, once clicked, lead to the September 7, 2012 Doodle.