Google has lost a case brought by a company whose name was being used my Adwords users. Insurance firm GEICO, who had not been using Adwords themselves, objected to Google allowing it's advertisers to use the term in their campaigns.
Note that A federal judge decided that Google is able to sell ads under the GEICO trademark, claiming that this is fair use of the trademark. GEICO's contention was that competing insurance companies were using the name GEICO under which to buy Google Ads, so that when someone searches for GEICO, their ad would come up.