A new app for the iPhone allows GEICO customers and others a number of features at the touch of a button.

GEICO’s GloveBox app, available at iTunes for free, allows the property-casualty insurer’s customers to pay their bill and even view their insurance card on their iPhone.

Even those who aren’t GEICO customers can find value in the app, the company says, because it includes  guidance on steps following an auto accident, how to change a flat tire and access other videos from the insurer.

Other features of the GloveBox app include a taxi/rental car finder, roadside services and GEICO contact information.

Jess Reed, the insurer’s chief information officer, said with the increasing popularity of the iPhone, “an iPhone app made perfect sense.

“We looked for capabilities that we think will add the biggest value to our customers,” Reed said. “Whether it’s on the Web, over the phone or with the new application via their iPhone, we want to provide the most convenient and best customer experience possible.”

GEICO (Government Employees Insurance Company) – as part of Berkshire Hathaway is the third-largest private passenger auto insurer in the United States, according to 2008 market share data from A.M. Best.