Google thought it had a right to own Groovle.com, so it took it's case to the National Arbitration Forum (NAF). (The NAF is an international arbitration service accredited by ICANN.)
But the NAF didn't agree with Google that Groovle could be confused for the search giant. Groovle does use Google's custom search. It also provides a service where you can skin your Google homepage with a photograph (similar to Bing without the hotspots).
Still, Groovle just didn't sound or act enough like Google to warrant the domain being handled over to the folks at Mountain View.