Critical Hit Rate
For melee weapons, critical hit rate is the sum of the base rate (5%), gear/atma (0100%), merit points (05%), Buffs, Weapon Skill modifiers, and player Dexterity relative to target Agility (also known as dDEX, 015%). As there is no cap to critical hit rate, it can be taken all the way to 100%, guaranteeing that every attack is a critical hit. Categoryspecific caps are marked. It also only takes whole number values, so it is impossible to have something like a 12.5% Critical Hit Rate. Weapon Skills with the description "Chance of Critical Hit varies with TP" modify Critical Hit Rate during Weapon Skill. Generally, the base modification at 100TP varies from 0% to 40%, and extra Critical Hit Rate is awarded for TP over 100. Example: A Thief has 115 Dexterity, Level 5 Critical Hit Rate Merits, +4% Critical Hit Rate in gear, and is fighting a monster with 96 Agility. They have a 5% + 4% + 5% + 0% + 2% (dDEX=19) = 16% Critical Hit Rate. For ranged weapons, critical hit rate is the sum of the base rate (5%), gear/atma (0100%), merit points (05%), Buffs, Weapon Skill modifiers, and player Agility relative to target Agility (also known as dAGI, no known cap). Dexterity does not affect critical hit rate for ranged weapons. 
Melee Critical Hit Rate (dDEX)
dDEX (Player DEX  Target AGI) determines the contribution of Dexterity to melee critical hit rate. This is added on to the base rate and merits to determine the total critical hit rate. Because this value depends on the target's Agility, which will be determined by its level and job combination, Critical Hit builds are sensible in some places and not sensible in others.
Based on the chart below, you can see that there is an extremely significant jump in critical hit rate when dDEX is increased from 40 to 50 (from 4% at dDEX=39 to 15% at dDEX=50), but no further boost to critical hit rate once dDEX is greater than 50.

Ranged Critical Hit Rate (dAGI)dAGI (Player AGI  Target AGI) determines the contribution of Agility to ranged critical hit rate. This is added on to the base rate and merits to determine the total critical hit rate. This value does depend on the target's Agility, but there are few times when critical hit rate builds are optimal (vs. times when they're less optimal) because adding the same amount of AGI always grants the same amount of critical hit rate and ranged critical hits are a constant multiplier of the damage you would have done otherwise.
This has been tested for the ranges of dAGI = 0~90. 
Merit Points
Notes

Job Points

Testing Critical Hit Rate
If you have something giving you an unknown amount of Critical Hit Rate, then the easiest way to find it is to use Abyssea Atmas and gear with known potency to force a 100% Critical Hit Rate. Lets say you have Y% known critical hit rate and X% from an unknown source. If you swing your weapon (or use your Weapon Skill) and get a noncrit return, you know that:
 100% > Y% + X%
Furthermore, if you manage to Critical Hit 303 times in a row, you can say with 95% certainty that your Critical Hit Rate is 100%. You can think of it like this:
 .99^n = Probability of Critical Hitting "n" times in a row if your critical hit rate is actually 99%.
Now, there's also a chance that you critical hit "n" times in a row with a 98% critical hit rate, so to accurately calculate the odds you have to add up all the .XX^n values over the range of possibilities. If you're using something like Razed Ruins and Gnarled Horn with 5 Critical Hit Rate merits, you know that your minimum Critical Hit rate is 75%. Then the equation would become:
 .99^n + .98^n + .97^n ... .75^n = Probability of Critical Hitting "n" times in a row if your Critical Hit rate is actually between 99% and 75%.
That equation happens to equal 95% when n = 303, hence the above statement.
Example: So say that you have a piece of equipment (like Assassin's Vest) with an unknown boost to Critical Hit Rate. The testing method would recommend you go to Abyssea, put on Atma of the Gnarled Horn, Atma of the Razed Ruins, and Atma of the Dark Depths (95% Critical Hit Rate with 5 merits) and the equipment. Swing away at something, and increase your critical hit rate by 1% per noncrit. The first sign of negative evidence (a noncrit) is enough to increment. At the final level, you should end up Critical Hiting 303 times in a row without seeing any regular hits, which makes you 95% confident that you've found your target value. From that point, you would add up your sources of critical hit rate and subtract them from 100%. The remainder is the critical hit rate on the equipment.
Past Critical Hit Rate tests relied on long parses against Hpmedes (N=10000+, as is seen in the references), Abyssea brought with it the possibility of a new way to test unknown Critical Hit Rate boosts. Overall, this is much faster than a similarly accurate Hpemde parse. On average, you would expect to swing 531 times to determine the critical hit rate of an unknown source with 95% confidence. The test will go much faster if you undershoot Critical Hit rate with your initial guess than if you overshoot it, and you should be able to get within 5% very quickly. This same method can be applied to Weapon Skills, using them as the X% unknown Critical Hit Rate.
Enhanced By
Abilities
 Rogue's Roll: Up to ~+20% critical hit rate depending on result.
 Blood Rage: +20% critical hit rate while in effect.
 Impetus: Up to +50% critical hit rate with consecutively landed attacks.
 Mighty Strikes: 100% critical hit rate while in effect.
Equipment
Item  Level  Slot  Jobs  Crit. Hit Rate 

Jupiter's Staff  51  Weapon  All Jobs  15% 
Thunder Staff  51  Weapon  All Jobs  15% 
Cruadin  69  Weapon  PLD DRK  15% (Campaign) 
Dies Irae  99  Weapon  WAR  10% 
Skadi's Attire Set +1  99  Set  THF BST RNG COR DNC  9% (max) 
Primate Staff +1  73  Weapon  MNK WHM PLD DRG  7% 
Barkborer  72  Weapon  BST  7% (vs. Plantoid) 
Ermine's Tail  72  Weapon  WAR THF PLD DRK BRD RNG SAM NIN DRG COR PUP DNC  7% (vs. Lizards) 
Eventreuse  72  Weapon  WAR  7% (vs. Plantoid) 
Koggelmander  72  Weapon  WAR RDM THF PLD DRK BST BRD RNG NIN DRG BLU COR  7% (vs. Vermin) 
Onishibari  72  Weapon  NIN  7% (vs. Beasts) 
Scheherazade  72  Weapon  DRK  7% (vs. Lizards) 
Zaide  72  Weapon  DRG  7% (vs. Beasts) 
Zonure  72  Weapon  WAR WHM PLD  7% (vs. Vermin) 
Kamewari  70  Weapon  SAM  7% (vs. Arcana) 
Anubis's Knife  65  Weapon  WAR THF DRK RNG NIN COR PUP DNC  7% (Poison) 
Athos's Armor Set  96~99  Set  MNK THF RNG NIN BLU COR PUP DNC  3~6% (Set) 
Smn. Doublet +2  90  Body  SMN  6% (Avatar) 
Destroyers  73  Weapon  WAR MNK RDM THF PLD DRK BST RNG DNC  6% (Latent) 
Gravedigger  73  Weapon  WAR BLM DRK BST  6% (Latent) 
Heart Snatcher  73  Weapon  WAR THF PLD DRK BRD RNG SAM NIN DRG COR PUP DNC  6% (Latent) 
Thyrsusstab  73  Weapon  WAR MNK WHM BLM PLD BRD DRG SMN SCH  6% (Latent) 
Dissector  72  Weapon  WAR RDM THF PLD DRK BRD RNG NIN DRG BLU  6% (Latent) 
GondoShizunori  72  Weapon  WAR SAM DRG  6% (Latent) 
Michishiba  72  Weapon  SAM NIN  6% (Latent) 
Morgenstern  72  Weapon  WHM PLD  6% (Latent) 
Rampager  72  Weapon  WAR DRK  6% (Latent) 
Retributor  72  Weapon  WAR DRK BST RNG  6% (Latent) 
Senjuinrikio  72  Weapon  NIN  6% (Latent) 
Subduer  72  Weapon  WAR PLD DRK  6% (Latent) 
Kumarbi's Akar  99  Body  WAR PLD DRK BST SAM DRG  5% 
Mustela Harness Set  96  Set  MNK THF RNG SAM NIN COR PUP DNC  5% (Set) 
Coruscanti  95  Weapon  THF BRD COR DNC  5% 
Iga Ningi +2  89  Body  NIN  5% 
Jing. Greatsword  87  Weapon  WAR DRK  5% 
Nvrch. Gants +2  87  Hands  COR  5% 
Hachiryu Haramaki  75  Body  WAR MNK RNG SAM NIN  5% 
Kawahori Kabuto  75  Head  MNK SAM NIN  5% (Blind) 
Skadi's Attire Set  75  Set  THF BST RNG COR  5% (Set) 
Rai Kunimitsu  74  Weapon  NIN  5% 
Kinkobo  73  Weapon  MNK WHM PLD DRG  5% 
Primate Staff  73  Weapon  MNK WHM PLD DRG  5% 
Asn. Jambiya  70  Weapon  WAR THF PLD DRK BRD RNG SAM NIN DRG COR PUP DNC  5% (Assault) 
Kumokirimaru  70  Weapon  SAM  5% 8% (vs. Vermin) 
Onikiri  65  Weapon  SAM  5% (vs. Demons) 
Kitsutsuki  64  Weapon  NIN  5% (vs. Plantoids) 
Arcanabane  59  Weapon  WAR DRK BST RNG  5% (vs. Arcana) 
Kidney Dagger  56  Weapon  WAR BLM RDM THF PLD DRK BST BRD RNG SAM NIN DRG SMN SCH  5% 
Asteria  99  Weapon  THF BRD DNC  4% 
Thaumas Hat  99  Head  MNK THF RNG NIN BLU COR PUP DNC  4% 
Usukane Haramaki +1  99  Body  MNK SAM NIN PUP  4% 
Laceratrice  95  Weapon  WAR  4% 
Lux Pugio  95  Weapon  THF BRD COR DNC  4% 
Bale Cuirass +2  89  Body  DRK  4% 
Oneiros Lance  88  Weapon  DRG  4% 
Nvrch. Gants +1  87  Hands  COR  4% 
Raid. Culottes +2  83  Legs  THF  4% 
Juogi +1  80  Body  MNK SAM NIN PUP  4% 
Smn. Doublet +1  75  Body  SMN  4% (Avatar) 
Hecatomb Subligar +1  73  Legs  WAR THF PLD DRK BST BRD DRG  1~4% 
Euxine Hat +3  99  Head  MNK THF RNG NIN BLU COR PUP DNC  3% 
Nefarious Collar  99  Neck  All Jobs  3% 
Wurrukatte Boots  99  Feet  MNK THF RNG NIN BLU COR DNC  3% 
Kacura Harness +1  96  Body  MNK THF RNG NIN BLU COR DNC  3% 
Asn. Vest +2  90  Body  THF  3% 
Mextli Harness  90  Body  MNK THF BST RNG NIN BLU COR PUP DNC  3% (Sphere) 
Iga Ningi +1  89  Body  NIN  3% 
Frn. Manoplas +2  87  Hands  BST  3% 
Ravager's Mask +2  85  Head  WAR  3% 
Iga Dochugappa  84  Back  NIN  3% 
Sylvan Bragues +2  83  Legs  RNG  3% 
Ferus Algol  80  Weapon  WAR DRK  3% 
Juogi  80  Body  MNK SAM NIN PUP  3% 
Afflictors  77  Weapon  WAR MNK BST NIN PUP  3% 
Leonine Mask  75  Head  WAR MNK THF BST NIN DNC  3% 
Organics  75  Weapon  WAR PLD DRK  3% 
Summoner's Dblt.  74  Body  SMN  3% (Avatar) 
Pygme Sainti  73  Weapon  PUP  3% 
Cletine  72  Weapon  DRG  3% 
Zahak's Mail  71  Body  WAR PLD DRK BST DRG  3% 
Fudo  70  Weapon  NIN  3% 
TonboGiri  68  Weapon  SAM DRG  3% (vs. Vermin) 
Claymore Grip  65  Grip  All Jobs  3% 
Nuevo Coselete  75  Body  WAR PLD DRK SAM DRG  3% 
Mirke Wardecors  75  Body  MNK THF BST RNG NIN BLU COR PUP DNC  3% 
Royal Redingote  75  Body  WHM BLM RDM BRD SMN SCH  3% 
Champion's Galea  75  Head  WAR PLD DRK SAM DRG  3% (Pet) 
Anwig Salade  75  Head  MNK THF BST RNG NIN BLU COR PUP DNC  3% (Pet) 
Selenian Cap  75  Head  WHM BLM RDM BRD SMN SCH  3% (Pet) 
Seiryu's Kote  75  Hands  WAR MNK BST BRD RNG SAM NIN  1~3% 
Valkyrie's Sabatons  75  Feet  WAR PLD DRK  1~3% 
Hecatomb Subligar  73  Legs  WAR THF PLD DRK BST BRD DRG  1~3% 
Shura Togi +1  73  Body  MNK SAM NIN  1~3% 
Grandoyne's Mail  99  Body  WAR PLD DRK BST SAM DRG  2% 
Euxine Hat +2  99  Head  MNK THF RNG NIN BLU COR PUP DNC  2% 
Kacura Leggings +1  96  Feet  MNK THF RNG NIN BLU COR DNC  2% 
Kacura Mittens +1  96  Hands  MNK THF RNG NIN BLU COR DNC  2% 
Calmecac Subligar  89  Legs  WAR PLD DRK BST SAM DRG  2% 
Frn. Manoplas +1  87  Hands  BST  2% 
Nemus Peti  87  Body  WAR RDM THF PLD DRK BST BRD RNG SAM NIN DRG BLU COR DNC  2% 
Nemus Peti +1  87  Body  WAR RDM THF PLD DRK BST BRD RNG SAM NIN DRG BLU COR DNC  2% 
Sylvan Bragues +1  83  Legs  RNG  2% 
Perle Hauberk  78  Body  WAR PLD DRK BST SAM DRG  2% 
Ebon Vest  71  Body  THF NIN DNC  2% 
Ebur Vest  71  Body  THF NIN DNC  2% 
Furia Vest  71  Body  THF NIN DNC  2% 
Nuevo Coselete  75  Body  WAR PLD DRK SAM DRG  2% (Pet) 
Mirke Wardecors  75  Body  MNK THF BST RNG NIN BLU COR PUP DNC  2% (Pet) 
Royal Redingote  75  Body  WHM BLM RDM BRD SMN SCH  2% (Pet) 
Kirin's Osode  75  Body  WAR MNK BST BRD RNG SAM NIN  1~2% 
Shadow Sabatons  75  Feet  WAR PLD DRK  1~2% 
Byakko's Axe  74  Weapon  WAR DRK  1~2% 
Shura Togi  73  Body  MNK SAM NIN  1~2% 
Kacura Subligar +1  96  Legs  MNK THF RNG NIN BLU COR DNC  1% 
Ebon Tights  71  Legs  THF NIN DNC  1% 
Ebur Tights  71  Legs  THF NIN DNC  1% 
Furia Tights  71  Legs  THF NIN DNC  1% 
Dilaram's Sollerets  95  Feet  WAR PLD DRK BST SAM NIN  8% 