How can I check warranty state of my iPhone?
Apple provides an online tool to check service and support coverage using your device's serial number.  You can find the serial number on your iPhone by tapping Settings > General > About.

SelfSolve.apple.com allows you to enter an Apple serial number and then see what warranty options are available.
The device does not need to be registered in order to be checked.

See below for an example of a MacBook Air that is still covered under AppleCare.