I have never been very good at running classic D&D dungeons, for two main reasons:
*I find it hard to be a neutral referee - I prefer to poke and prod the players, engaging with the goals and the weak spots of their PCs ("indie"-style);
*Related to the above, I am not a big fan of adjudication that relies heavily on GM extrapolation of the fiction - it can easily become a bit adversarial, especially if the difficulty the PCs find themselves in is a result of me as GM having poked or prodded the players into a situation!
But recently I've been running 
Torchbearer 2nd ed. In TB the players never suffer a loss or setback without a check against an obstacle to see what happens (they can succeed without a check if the GM determines that their declared actions are a "good idea" - though players have reasons to want to make checks, because only by making checks and either succeeding or failing can they advance their skills and attributes). The GM has to adjudicate the fiction, but for the purposes of (i) setting obstacles, and (ii) extrapolating failure consequences. It doesn't have the unmediated character of adjudicating fiction that is found in classic D&D. So it's much better for a GM like me!
Referring to UngainlyTitan's post: in Torchbearer, it is stuff on PC sheets - skills, attributes, and the gear that enhances them (eg rope helps appropriate Dungeoneer checks) or that is otherwise necessary (light sources, food) - that lets players succeed. But it doesn't allow 
bypassing challenges without interaction. Players can't declare an action except by describing what in the fiction their PC is doing to overcome an obstacle. Only then is the difficulty set, and the player's dice pool put together and rolled.