Nokia Lumia 820 - How can I silence an incoming call on my Nokia Lumia phone?

During an incoming call, before the call is answered, use the volume up/down button to silence the device without rejecting the call. You can still answer or ignore the call as normal afterwards, as long as the caller does not end the call, or the call has been diverted to voicemail.

Nokia Lumia Amber update does bring Flip-to-silence feature, which allows you to silence the ringer by flipping the phone face down. This feature can be switched off by going to Settings > Audio > Enhancements and then slide Flip to silence toggle switch to the left.