Diceless D&D

Or Talking Your Way Through The Dungeon
Ultimately Role-playing is just that - talking in first person as the character, or describing what the character says and does in third person. From White Box forward the game is a talking game, a social activity. The balance between rolling dice to determine outcomes ("roll-playing") and talking back and forth between players and referee to determine outcome is something that varies from group to group and session to session. Some sessions are mostly talking and it is certainly possible to do away with rolling the dice, should all the players agree to do so. Randomness is gone and outcomes are decided purely on the merit of the argument presented by players to the referee. I daresay this isn't the norm, however.
White Box and the hobby has its roots in wargaming where a long tradition exists of using dice to introduce random outcomes and add excitement and uncertainty. Negotiating with NPCs and monsters, questioning prisoners and the occasional sage, even bargaining with the local magistrate or merchant are certainly meant to be part of the game, but the talking need not stop with those activities. Even among a group that prefers to make a lot of dice rolls, after-all it is fun to see what the dice give us and play off the random result, a well described plan of action can however add to the excitement and shared mental visualization upon which the game depends as well. Clever thinking can even substitute at times for combat rolls.
On a recent dungeon crawl my fantasy compatriots and I (well, my player character) managed to take out the bulk of the undead baddies with an improvised Molotov and the body of a big dead critter by dropping each in succession and from great height onto the unwary (but hungry) undead who waited below for us to descend into darkness (and become their feast). We settled on and described our plan verbally. No roll needed. Splash - zombies afire and burned away. Crunch - skeletons crushed beneath the massive weight of a great dead thingy. Rather than looking on a weighty character sheet for answers to life's "in game" problems, why not turn instead to player imagination?
Early in the games history, gamers looked at player skill as something like having skill at chess - an ability to masterfully play the game. Skill wasn't a number on the character sheet. We used player skill during the game to solve problems encountered by our characters and acquire treasures while minimizing risk, not before or after the game cleverly crafting the values and combos on the character sheet. That style of play comes later with more involved chargen and expanded rules allowing greater character customization.
Today we have many choices to make about how to "play the game". Pre-Dragon Lance, it was common for story to be what develops at the table, perhaps helped along by the referee revealing some (small amount of) world background detail which the players then incorporate into their memories of the session. Balancing encounters - not a thing. If, as referee, I wanted to toughen/weaken an encounter, adjusting the critter's remaining Hit Points on-the-fly usually did the trick...or add in some reinforcements, or fail a morale check. All the while encouraging table talk. "What do I see?" followed by "What do you want to do?" is a wide-open creative way to play the game that can still produce an enjoyable time for all involved.