Critical strike
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A critical strike is a modifier that causes an attack to deal twice its normal damage. This could represent an attack that hits harder, a lucky strike or damaging a weak area on an opponent.
Most champions have different attack animations for a critical strike, though some do not; this includes mages and other champions not meant to be built using autoattacks for damage. Some of these champions performing a critical strike (if built being able to perform them) may instead have a soundbite that plays in place of an animation, typically a grunt of effort.
Players can increase the chance and the damage of critical strikes with items, abilities, and runes.
It only applies to basic attacks or certain abilities like Gangplank's Parrrley and Yasuo's Steel Tempest that act like a basic attack or Garen's Judgment, which is something unique.
Critical strike is valuable for all champions who primarily deal damage with automatic attacks, rather than through abilities. Some champions, such as Ashe, have an affinity for critical hits and benefit more from items that improve them.
It's important to note that you cannot score a critical strike against a building such as a turret or inhibitor.
Chance
Critical strike chance is the chance of a champion's physical attacks dealing a critical strike. Critical strike chance stacks additively. Runes, items and all abilities can increase critical strike chance.
When averaged over a large number of autoattacks and at base critical damage, critical strike chance is essentially a damage multiplier where each % of crit chance adds 1% damage. Thus at 50% critical strike chance a champion will be doing (on average) 150% damage with autoattacks, not counting critical strike damage. Because of this, critical strike chance scales well with both attack damage and attack speed. The formula for this damage multiplier is given by:
% Damage multiplier = %Crit chance x (%Crit Damage  100%) + 100%
The maximum critical strike chance you can reach at level 1 through masteries is 20.25%, excluding abilities and items.
Critical strike chance has a hard cap at 100%.
Critical strike chance has a theoretical gold value of 50 gold per 1% critical strike chance. This makes Cloak of Agility the most efficient core item for critical strike chance, as it grants 15% critical chance for the cost of 730 gold with a 48.6 gold per % crit chance efficiency.
Increasing critical strike chance
Items
Core
 Atma's Impaler: +15% critical strike chance, +45 armor. Unique Passive: You gain attack damage equal to 1.5% of your maximum health. 2300 gold.
 Avarice Blade: +10% critical strike chance. Unique Passive  Avarice Gain +3 gold per 10 seconds. Unique Passive  Greed: gain an additional 2 gold on every kill. 800 gold.
 Brawler's Gloves: +8% critical strike chance. 400 gold.
 Cloak of Agility: +15% critical strike chance. 730 gold.
 Executioner's Calling: +20% critical strike chance, +25 attack damage. Unique: your basic attacks inflict Grievous Wounds on enemy champion for 1.5 seconds. 1900 gold.
 Phantom Dancer: +30% critical strike chance, +50% attack speed, +5% movement speed. Unique Passive: Your champion ignores unit collision. 2800 gold.
 Statikk Shiv: +20% critical strike chance, +40% attack speed, +6% movement speed. Unique Passive: Moving and attacking builds Static Charges. At 100 charges, your next attack expends the charges to deal 100 magic damage to up to 4 targets. This damage can critically strike. 2500 gold.
 Sword of the Divine: Active: You gain 100% attack speed and 100% critical strike for 3 seconds or 3 critical strikes  60 second cooldown. +45% attack speed. Passive: This item does not grant any attack speed while on cooldown. Champion kills reduce the current cooldown by 50%. 2150 gold.
 Trinity Force: +10% critical strike chance, +30 ability power, +30 attack damage, +30% attack speed, +250 health, +250 mana, +8% movement speed.Unique Passive  Rage: Basic attacks grant 20 movement speed for 2 seconds on hit. Minion, monster, and champion kills grant 60 movement speed for 2 seconds. . Unique Passive  Spellblade: After using an ability, your next basic attack deals bonus damage equal to 200% of your base attack damage (2 second cooldown). 3703 gold.
 Youmuu's Ghostblade: +15% critical strike chance, +30 attack damage, +10% cooldown reduction, +20 armor penetration. Unique active: +40% attack speed and +20% movement speed for 6 seconds (4 seconds for ranged champions)  45 second cooldown. 2700 gold.
 Zeal: +10% critical strike chance, +20% attack speed, +5% movement speed. 1100 gold.
Variable Availability
 SH Infinity Edge: +25% critical strike chance, +80 attack damage. Unique Passive: +50% critical strike damage. 3800 gold.
 TC Lord Van Damm's Pillager: +25% critical strike chance, +80 attack damage. Unique Passive: +50% critical strike damage. 3800 gold.
 TC Wicked Hatchet: +10% critical strike chance, +20 attack damage. Unique Passive: Critical strikes causes your target to bleed for an additional 60% of your bonus AD as physical damage over 3 seconds. 1200 gold.
Champion abilities
(Note that any ability boosting attack speed has an indirect impact on the number of crits)
 Ashe's Focus gains 4 / 5 / 6 / 7 / 8 Focus stacks per second after not dealing damage in the last 3 seconds. At 100 stacks, Ashe will critically strike on her next basic attack. Thereafter, Focus stacks will reset to an amount equal to her critical strike chance.
 Pantheon's Certain Death grants him 100% critical strike chance against targets below 15% of their maximum health.
 Shaco's Deceive grants him 100% critical strike chance on his next attack, but for modified critical damage: 40 / 60 / 80 / 100 / 120%.
 Tryndamere's Battle Fury passively increases his critical strike chance by 0.35% per point of Fury he currently has.
 Yasuo's Way of the Wanderer doubles his critical strike chance, but the damage dealt by his critical strikes is reduced by 10%.
Runes
 Critical Chance runes increase critical strike chance.
Damage
Critical strike damage refers to the amount of damage that a champion's critical strike will deal. All champions have 200% critical strike damage by default, except Yasuo who has 180% to compensate for his doubled crit chance. In most cases, critical strike damage stacks additively. Damage modifiers apply to critical strike damage normally.
Modifying Critical Strike Damage
 Champion Abilities
 Shaco's Deceive modifies his base critical strike damage to 140 / 160 / 180 / 200 / 220% from the default of 200%.
 Yasuo's Intent multiplicatively reduces by 10% his total critical strike damage (e.g. 200% to 180%).
Items
 SH Infinity Edge: Unique Passive: +50% critical strike damage. +80 attack damage, +25% critical strike chance. 3800 gold.
 TC Lord Van Damm's Pillager: Unique Passive: +50% critical strike damage. +80 attack damage, +25% critical strike chance. 3800 gold.
Runes
 Critical Damage Runes
 Marks: +1.24% / +1.74% / +2.23% (primary)
 Seals: +0.43% / +0.61% / +0.78%
 Glyphs: +0.31% / +0.43% / +0.56%
 Quintessences: +2.4% / +3.47% / +4.46%
Notes
 The maximum bonus critical strike damage obtainable is as follows:
 Runes: 45.51%
 Items: 50%
 For most champions, the maximum critical strike damage available is 195.51% for a total of amount of 295.51% damage on their critical strikes.
 Including the additional 20% base critical strike damage from rank5 Deceive, Shaco's will deal 315.51% damage on his critical strike. Including the 20% damage modifier from Backstab, this is further increased to 378.61% damage.
 Including the 130% damage modifier from rank5 Hyper Charge, Jayce's critical strikes will deal 384.15% (130 * 2.9551) damage.
Skills affected by Critical Chance
Certain skills are capable of Critical Strikes and/or are affected by Critical Chance, however these skills may bound to certain limitations. E.g. Poppy's Devastating Blow will gain critical damage bonus only based on her attack damage, and the bonus damage part of the skill is not accounted.
Below is the list of skills that are capable and affected by critical strikes and chances.
 Darius's Crippling Strike: Only base attack damage component gain critical damage bonus.
 Gangplank's Parrrley: The entire damage including its bonus damage component can critically strike.
 Garen's Decisive Strike: Only bonus damage provided by your AD (ie: not base damage of Decisive Strike) can critically strike.
 Judgment: Only bonus damage provided by your AD (ie: not base damage of Judgment) can critically strike.
 Lucian's Lightslinger: The additional shot is capable of critically striking like a normal auto attack.
 Master Yi's Double Strike: The additional strike is capable of critically striking like a normal auto attack.
 Alpha Strike: Only bonus damage provided by your AD can critically strike.
 Nautilus's Staggering Blow: Only base attack damage component gain critical damage bonus.
 Nidalee's Takedown: Only base attack damage component gain critical damage bonus.
 Poppy's Devastating Blow: Only base attack damage component gain critical damage bonus and applied as magic damage.
 Rengar's Savagery: Only base attack damage component gains critical damage bonus.
 Shaco's Backstab: Damage bonus increases damage after critical modifier.
 Shyvana's Twin Bite: Only applicable to first hit.
 Talon's Mercy: Damage bonus increases damage after critical modifier.
 Noxian Diplomacy: Only base attack damage component gain critical damage bonus.
 Tryndamere's Spinning Slash: Cooldown is reduced by 1 second for every critical strike. This effect is doubled against champions.
 Wukong's Crushing Blow: Only base attack damage component gain critical damage bonus.
 Xin Zhao's Three Talon Strike: Only base attack damage component gains critical damage bonus.
 Yasuo's Steel Tempest: Only bonus damage provided by your AD (ie: not base damage of Steel Tempest) can critically strike.
Miscellaneous
Other skills that may OR may not be affected by critical strikes and chances, due to other reasons.
 Anivia's Frostbite: Although the 2x damage modifier applied by being chilled by Flash Frost is given out as critical strike, It is unaffected by critical damage modifiers such as Infinity Edge.
 Pantheon's Spear Shot: Will crit for a +100% damage bonus due to the passive from Certain Death if the target is under 15% health, also crit damage modifiers (such as Infinity Edge) apply to this in fact.
 Shaco's Deceive: Causes next autoattack during the next 6 seconds to deal increased damage, which is described as a "Critical Strike", and is affected by any other modifier such as Infinity Edge.
 Vayne's Condemn: The doubledamage proc'd by being knocked into a wall is given out as critical strike, despite being unaffected by critical damage and critical strike.
 Karthus's Lay Waste: Appears like a critical strike when acting like a single target spell (hitting only one enemy) although it is unaffected by critical damage modifiers such as Infinity Edge.
Champion statistics  

Offensive 

Defensive  
Magical  
Movement 