Better Criticals

Better Criticals is a perk in Fallout, Fallout 2, Fallout 3, Fallout: New Vegas, Fallout 4, and Fallout Tactics.

Fallout, Fallout 2 and Fallout Tactics
With this perk, a +20 bonus is applied to the Critical Hit table roll, which effectively moves it up one table entry, ensuring a more damaging type of hit.

Bugs
Scripts triggered by a critter's death do not fire upon "instant-death zero-damage criticals" (Pariah dog is one example). These can be prevented by also having the Living Anatomy perk which makes zero-damage attacks impossible. Allegedly, Bonus HtH Damage and Bonus Ranged Damage perks do the same.

Fallout 3 and Fallout: New Vegas
With this perk, the weapon's critical damage is increased by 50%.