In an RPG, a phenomenally successful hit in combat, typically landing in some vital region, hence the name. Typically critical hits do more damage than regular ones; in some systems, special side-effects are suffered depending on where you were hit, what you were hit with, etc.

Critical hits were introduced to D&D in the third edition. The 3rd Edition D&D critical hit system is as follows: when you roll a certain number naturally (usually limited to 20s, though some weapons have a better threat range), that's considered a threat. When you score a threat, you roll again; if you manage to score any successful hit against the target on this role, you've scored a critical hit. Most weapons deal double damage on a crit. However, some creatures, such as any undead, are immune to critical hits.

Feel free to explain critical hit systems from other role-playing games here.