What Mechanics Support Role Playing in an RPG?
this is a great question. unfortunately I don't know that there are many mechanics of the game system in dnd that promote role playing (my main experience with rpgs, so the only example I can use). this makes a certain amount of sense as it was based on wargaming in the beginning, and was a way to widen the berth of what could be experienced with table top miniature war games (someone correct me if ive got my history wrong).
with that caveat im trying to decide what rules in the dnd books may be used to encourage role playing, even if that wasn't its original intent. talon mentioned the main way it can be expressed, i.e. awarding experience points. perhaps then other rewards can be looked at as well.
role playing then opens the door (and may be the only way to open it) to other npc's, other adventures, other information, anything that rewards the character's role playing with something related to what has been role played. if the character role plays themselves out of a sticky situation (avoiding combat), the reward can range from full experience points for the thing avoided (creature, npc trap, etc). but then more can be obtained, depending upon how the player role played. a sliding awards scale, as it were.