Critical hits are physical attacks that hit crucial spots, dealing a significant amount of additional damage.
Melee critical hits always deal double damage. For the PC there is a base chance of approximately 5% that a hit becomes a critical hit. This chance can increase to around 15% if the PC has good luck. PCs with the find weakness skill, certain weapons and items, and certain class powers receive additional chances to crit. These chances will be individually doubled if the PC is attacking with a murderous weapon. Slaying melee weapons always score criticals against the creature type they slay.
For the PC, a critical hit is signified by the expression "with full force", for instance "You hit the giant rat with full force and slay it". For monsters, the message simply changes to "The <creature> critically hits you."
A melee critical hit always deals double damage unmodified by PV. Modified by PV, it will almost always turn out to have a greater effect than that. For instance, if a normal blow would have dealt 40 damage but the monster had 30 PV, a critical hit would end up dealing quintuple damage compared to a normal hit.
As critical hits do not normally bypass PV, it is possible to receive the "You hit the <creature> with full force but do not manage to harm it." message. In such a case even the double amount of damage wasn't enough to get past the monster's PV. Consider switching to a different form of offense.
If a critical hit landed by a monster would bring the PC's HP below 0, having good luck will often prevent this death by instead bringing the PC's HP to 1. This effect only seems to come into play when the PC is above a certain flat HP threshold, and applies to both melee and ranged criticals. This does not occur if a non-critical hit takes the PC out.
Missile critical hits behave somewhat differently. The base chance for a critical is lower (~3-10% depending on luck), and appropriate sources of increased critical hit chance, including find weakness, seem to be around half as effective on ranged attacks. The damage modifier is different from melee — missile criticals can deal double, triple, quadruple or even quintuple damage. It is not known whether the same is true for monsters; what is known is that high level monsters that use missiles (such as fire giant kings or titans) can deal great amounts of damage at a distance, possibly for this reason.
Slaying missiles guarantee critical hits against the proper monster types. They also add extra damage if used against appropriate monsters (e.g. you can roll normal criticals with arrows of jelly slaying, but if the monster was not a jelly it won't affect the modifier), changing the multiplier to from triple to sextuple (x6). Slaying ammunition is thus even more destructive as a method to defeat certain enemies than melee weapons. For characters that are very skilled at using their missile weapon to begin with (especially Archers), the combination with slaying ammunition can result in one-hit kills of even the most powerful creatures.
Scoring a critical with missiles is signified by the term "exactly", as in "You exactly hit the <creature>". Monster missile critical hits yield the message "You are critically wounded." instead of "You are wounded." following "The <creature> shoots a <missile> at you!".
Critical hits should not be confused with penetration effects, i.e. hits that bypass PV. Critical hits do not in themselves bypass PV. It is possible for monsters' attacks to both penetrate armor and score a critical hit.
The message "the <creature> targets a vital spot and hits you" also does not signify a critical hit; this means that the monster's attack bypassed the PC's PV whilst (s)he was wearing light body armor. The message "the <creature> punches through your armor" is generated for attacks bypassing heavier body armor.