More glancing blows (and near-saves)

 A quick rule for any D&D game. I'm certainly not the first one to suggest the "half damage" part.

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Glancing blows

When you roll the exact number needed to hit the target's AC, this is a glancing blow.

You damage is halved.

If the target has more than 1 HP before the hit, the glancing blow can reduce it to 1 HP, but no less.

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This is the gist of it, but we could change the specifics. 

Instead of half damage, for example, I might do "one third of your maximum damage" to save myself a roll (and further differentiate 1d6+1 from 1d8 damage). 

Likewise, the "1 HP" part probably needs a few exceptions, but it would be fun if even a peasant has a 5% chance to survive being hit by a powerful monster and live to tell the tale (even if unconscious, maimed, etc.  -the idea is that a glancing blow doesn't kill).

You could extend the same reasoning to saving throws. This is somewhat similar to what I've been doing in my games. When the MU casts an 8d6 fireball, I make a roll even if the target is a group of goblins, allowing a natural 20 to save some of them. I might call this rule "there is always a save".

D&D 4e had minions rules that worked in a similar way: "minions" had only 1 HP but wouldn't be killed if they made a successful save. 

I think my version feels a bit less artificial. No goblin should resist TWO 8d6 fireballs! Also, REDUCING a foe to 1 HP is a great opportunity of surrender, retreat, parlay, etc.

I also like making glancing blows a common concept so my players can finally accept I'll eventually tell them the monster's AC, so they might as well stop asking if they hit!

Anyway, for now this is just a random thought.