Diablo 3 has kept the same amount of armor slots as Diablo 2.
These include places for boots, body armor, gloves, belts, helmets, two ring slots and an amulet.
Each time body armor or helmet armor is changed, it will change the appearance of your character. Because of this fundamental property that all items (especially armor) have, the ability to customize your character's apprearance outside of weapons and armor is almost zero. At character creation you can choose either a male or female character, but from there one can only guess how to change the appearance of the character at this point.