Monopolies themselves aren't illegal. To be convicted of an antitrust violation, a firm needs to both have a monopoly and needs to be using anticompetitive means to maintain that monopoly. The recent "textbook" example was of Microsoft, which in the 90s used its dominant position to charge computer manufacturers for a Windows license for each computer sold, regardless of whether it had Windows installed or was a "bare" PC.

Depending on how you define the market, Google may not even have a monopoly. It's probably dominant enough in web search to count, but if you look at its advertising network it competes with Facebook and other ad networks. In the realm of travel planning (to pick an example from these comments), it's barely a blip.

Furthermore, Google can potentially argue it's not being anticompetitive: all businesses use their existing data to optimize new products, so Google could claim that it not doing so would be an artificial straightjacket.