Wired has an article about the design of Google's logo and its iterations. "Ruth Kedar, the graphic designer who developed the now-famous logo, shows the iterations that led to the instantly recognizable primary colors and Catull typeface that define the Google brand. Kedar met Google co-founders Sergey Brin and Larry Page through a mutual friend nine years ago at Stanford University, where she was an assistant professor."
In the process, Ruth used a lot of symbols: from a pattern that suggests the infinite to interlocking rings that symbolize the power of search to transgress cultures, from a happy magnifying glass to sheer playfulness. "By taking out the magnifying glass, Kedar opens up the logo to signify that Google can become much more than just a search engine. By playing with the angles and colors of the letters, she tries to make clear that Google isn't a square corporation."
Ruth Kedar explains that she chose the Catull typeface because "Catull borrows elements from traditional writing instruments such as the quill and the chisel with a modern twist. Search, by nature, is an activity that requires we look into the past. Therefore Catull's historical ties seemed appropriate, as did the bridging between the old analog world and the new emerging digital era."
As you can see, the simple and cheerful Google logo hides a lot of interesting ideas and it's still relevant to the company, even if it's no longer just a search engine.
Before adopting a professional logo, Google used a logo created by Sergey Brin in GIMP. "Tinkering one day with a graphics program called GIMP, Sergey created a color rendering of the Google letters with an exclamation point at the end, mimicking Yahoo! He seemed quite proud of the new logo, which was composed of kindergarten-style block letters in primary colors. But it wasn't the look that meant the most to him. He was pleased that he had been able to teach himself how to use GIMP, free software that was tricky to employ," writes David A. Vise in The Google Story.