As previously mentioned, it is the mobs that really make or break your experience while playing this game.
Sure, there are a number of passive characters, such as chickens, pigs, and even horses, but it is the ones that can, and will, attack you that make things interesting.
Unlike the crazed Creeper, that will attack you on site, the Enderman starts out relatively neutral. If, however, you look directly into the eyes of this eerie mob, it will attack; ultimately showing you no mercy.
You will know when you have incurred their wrath when you hear them scream this incredibly spooky and loud sound. The Enderman will then freeze for a few seconds, during which time, you really should be running as far away as you can; little good that it will do you.
While it is certainly true that running will work against many hostile mobs, these guys will simply continue to pursue you until it, or you, is dead. You can, if you get lucky, try and cross a stream; they hate water which causes them significant damage.
You can also try and get another hostile mob, such as the Creepers, to attack them although I have never personally had much luck with that approach!