One reason 3 A.M. might be such an infamous time is because it is sometimes associated with REM sleep. The brain begins to process events somewhat differently during this time which can lead to a sensation of something odd taking place. During this stage of sleep, Sleep Paralysis can occur. Auditory hallucinations are apparent during this time and noises such as knocking, laughing, scratching, and footsteps may appear. It's easy to see how this brain activity can make us jump to the conclusion that a demon is right outside our door.
http://themindseye.wordpress.com/2006/04/15/3am/
http://www.ouijaboardrules.com/2011/01/ouija-board-rules-3am-devils-hour.html
http://www.paranormalpeopleonline.com/dead-time-is-it-a-dead-myth-or-cold-fact/
http://www.youtube.com/watch?v=4NO7xA4x9kM