Google CEO Eric Schmidt believes that Bing, and not Facebook, nor Apple, is Google's biggest competition. "For years people would ask about Microsoft, and now everyone has forgotten about Bing, but again Bing is a well run, highly competitive search engine," Schmidt told The Wall Street Journal. He also makes sure to make some jabs at Apple over its closed system approach and mentions that users should give their information to Google instead of Facebook. Many believe that Google's increasing presence in social networking and in mobile mean that its biggest competitors are Facebook and Apple. Overall though, Schmidt says that the tensions Google has with the two companies are not competitive threats to the search giant.
Bing recently passed Yahoo in search market share, right before it started to power the web giant's search results. This essentially means that Bing, with or without Yahoo, is now only second to Google, though still a distant second. See Schimdt talk about Bing at around the third minute:
Although Bing is still nowhere near Google in market share, the decision engine (as Microsoft likes to call it) is slowly but steadily gaining. Search is still Google's primary business, so Schmidt does have a point: Bing is cutting into Google's main revenue stream. Microsoft is pushing innovation efforts hard with Bing, causing Google to step up its game.