In general, damage is calculated this way:

{((BaseDamage * A) - (Defense * rand(0.5, 0.6))) * (Skill * B + Critical) * C} * D

where:
- BaseDamage is a random number selected from a base damage range (see Base Damage Equations),
- A, B, C, and D are modifiers (see Modifiers),
- Defense is PDDamage for physical attacks and MDDamage for magic attacks; also see Level Disadvantage under Modifiers > A which has a defense-like effect,
- Skill and Critical are expressed as decimals, such that a 260% damage skill is 2.6 (see Critical),
- Skill is equal to 1 if no skill or a magic skill is used, and
- {X} restricts the value of X to the range [1, 199999] and removes its fractional part.

There are certain exceptions to the general formula, outlined below:

No critical: Blizzard, Shadow Meso, Assassinate first 3 hits
Ignores defense (but not dLevel modifier): Assaulter, Sacrifice, Demolition, Phoenix/Frostprey/Octopus/Gaviota

Weapon Damage:
Max = (Primary + Secondary) * WeaponAttack / 100
Min = (Primary * Mastery * 0.9 + Secondary) * WeaponAttack / 100
where:
Primary and Secondary vary depending on the weapon (see Weapon Modifiers below),
Mastery is weapon mastery as a decimal, such that 60% mastery is 0.54, and
WeaponAttack is the sum of all equips, and includes projectiles if and only if they are consumed during the attack.

For the rest of this post I will use the notation: rand(min, max). Using this convention the general Weapon Damage equation can be expressed in one line:
(Primary * rand(Mastery * 0.9, 1) + Secondary) * WeaponAttack / 100

Weapon Modifiers:

Weapon	Primary	Secondary
One Handed Sword	STR * 4.0	DEX
One Handed Axe/BW/Wand/Staff (Swinging)	STR * 4.4	DEX
One Handed Axe/BW/Wand/Staff (Stabbing)	STR * 3.2	DEX
Two Handed Sword	STR * 4.6	DEX
Two Handed Axe/BW (Swinging)	STR * 4.8	DEX
Two Handed Axe/BW (Stabbing)	STR * 3.4	DEX
Spear (Swinging)	STR * 3.0	DEX
Spear (Stabbing)	STR * 5.0	DEX
Polearm (Swinging)	STR * 5.0	DEX
Polearm (Stabbing)	STR * 3.0	DEX
Dagger (Non-Thieves)	STR * 4.0	DEX
Dagger/Throwing Stars (Thieves)	LUK * 3.6	STR + DEX
Bow	DEX * 3.4	STR
Crossbow	DEX * 3.6	STR
Knuckle	STR * 4.8	DEX
Gun	DEX * 3.6	STR

Magic:
((Magic * 0.058)^2 + Magic * 3.3 * rand(Mastery * 0.9, 1) + INT * 0.5) * SpellAttack / 100

Heal Damage:
(INT * rand(0.3, 1.2) + LUK) * Magic / 200 * TargetMultiplier
The % listed in the skill description (300% at max) acts as the Skill value (see General Damage Calculation above)

Heal Target Multiplier: 0.3 + 1/NumTargets (including yourself)
1: 1.3
2: 0.8
3: 0.633
4: 0.55
5: 0.5
6: 0.467

Dragon Roar:
(STR * 4.0 * rand(Mastery * 0.9, 1) + DEX) * WeaponAttack / 100

Lucky Seven/Triple Throw:
(LUK * rand(2.5, 5.0)) * WeaponAttack / 100

Bow (Swinging) / Power Knock Back:
(DEX * 3.4 * rand(0.09, 1) + STR) * WeaponAttack / 150

Claw (Punching):
(LUK * rand(0.09, 1) + STR + DEX) * WeaponAttack / 150

Gun (Punching):
(DEX * rand(0.09, 1) + STR) * WeaponAttack / 200

Bare Hands:
(STR * J * rand(0.09, 1) + DEX) * WeaponAttack / 100
WeaponAttack equals floor((2*level+31)/3) and is capped at 31.
J equals 3.0 for Pirates and 4.2 for all 2nd+ job Pirates.

Phoenix/Frostprey/Octopus/Gaviota:
(DEX * 2.5 * rand(0.7, 1) + STR) * AttackRate / 100

Critical is normally additive to the skill percentage. For the canonical example, Double Shot is 130% with no critical, and 230% with +100% critical.

Sharp Eyes adds an additional 100%, for +140% to base critical when maxed. When combined with Stun Mastery, a further 100%, totalling to Stun Mastery + Sharp Eyes + 200%, or +300% when both are maxed.

Corsair's Elemental Boost also acts as "critical" in that it is additive to the skill percentage, so it is +200% when maxed.

Venom:
Damage per second tick = (rand(8.0, 18.5) * [STR + LUK] + DEX * 2) / 100 * BasicAttack

Ninja Ambush:
Damage per second tick = (STR + LUK) * (1.5 + (SkillLevel * 0.05))

Shadow Web:
Damage per 3-second tick = MonsterHP / (50 - SkillLevel)

Flamethrower:
Damage per second tick = InitialHitDamage * (5% + AmpBulletDamage%)

Shadow Meso:
Damage = 10 * Mesos * SpecialCritical (in skill description; ignores regular critical)

Meso Explosion:
if Mesos <= 1000, then Damage per bag = (50 * Mastery) * rand(0.5, 1) * ((Mesos * 820 + 28000) / 5300)
if Mesos >= 1000, then Damage per bag = (50 * Mastery) * rand(0.5, 1) * ((Mesos * 50000) / (Mesos + 5250))

note: Mastery = X/1000, where X is the internal skill variable.

Chakra Recovery:
Base = (LUK * 6.6 * 0.5 + DEX) * (SkillRecovery + 1) / 5

Heal Recovery:
Recovery = something * Magic * HealLevel * TargetMultiplier

Heal Target Multiplier: 0.3 + 1/NumTargets (including yourself)
1 - 1.3
2 - 0.8
3 - 0.633
4 - 0.55
5 - 0.5
6 - 0.467

Nekonecat's old equation:
Max = (1.132682429*10^-7*luk^2 + 3.368846366*10^-6*luk + 1.97124794*10^-3) * magic * int * healSkillLevel * multiplier
Min = MAX*0.8

Poison Brace/Poison Mist/Fire Demon/Ice Demon:
Damage per second tick = MonsterHP / (70 - SkillLevel)

Weapon Damage:
PADamage^2 * rand(0.0085) - WDEF*A - (WDEF-StandardPDD)*B

where:

A = C + 0.28

if WDEF >= StandardPDD, then B = (C*28/45 + (CharacterLevel)*7/13000 + 0.196)
if WDEF < StandardPDD, then B = D * (C + (CharacterLevel)/550 + 0.28)

C (warriors) = STR/2800 + DEX/3200 + INT/7200 + LUK/3200
C (everyone else) = STR/2000 + DEX/2800 + INT/7200 + LUK/3200

if Character Level >= Mob Level, then D = 13/(13 + CharacterLevel - MobLevel)
if Character Level < Mob Level, then D = 1.3

StandardPDD values can be found here.

Magic Damage:
MADamage^2 * rand(0.0075, 0.008) - (MDEF/4 + STR/28 + DEX/24 + LUK/20) * K
where K = 1.2 for magicians and 1 otherwise.

Physical Accuracy:

HitRate = (13 - Avoid / Accuracy * (dLevel + 25.5)) / 6
FullAccuracy = Avoid * (dLevel + 25.5) / 7
MinAccuracy = Avoid * (dLevel + 25.5) / 13
where dLevel = MobLevel - CharLevel, and 0 if negative

Magical Accuracy:

HitRate = (12 - Avoid / Accuracy * (dLevel + 25.5)) / 7
FullAccuracy = Avoid * (dLevel + 25.5) / 5
MinAccuracy = Avoid * (dLevel + 25.5) / 12
where
Accuracy = (floor(INT/10) + floor(LUK/10)) * 5, and
dLevel = MobLevel - CharLevel, and 0 if negative

Leech conditions: At least one of the following must be met in order to share a cut of party EXP
1. Deal at least 1 damage to the monster.
2. Be within 5 levels of the monster.
3. Be within 5 levels of a party member that fulfills 1 or 2.

EXP received when partied = Monster EXP * (0.4 * Player level / Total party level + 0.6 * Damage dealt / Monster HP) * Party bonus
(Total party level = sum of the levels of all players that satisfy leech conditions. When not partied, you count as your own party, i.e. you get all the EXP.)
(In order words, 60% is split proportional to damage dealt and 40% is split proportional to character level.)

EXP recieved when not partied = Monster EXP * (Damage dealt / Monster HP)
(In order words, all EXP is split proportional to damage dealt.)

If your party is not the only one who dealt damage:
EXP received when partied = Monster EXP * (Damage your party dealt / Monster HP) * (0.4 * Player level / Total party level + 0.6 * Damage dealt / Damage your party dealt) * Party bonus
(It's the same as treating each party as a separate unpartied individual and then splitting within each party.)

Character
1: 15
2: 34
3: 57
4: 92
5: 135

6 ≤ level ≤ 50:
if level%3 = 0, exptnl(level) = (level^4 + 57*level^2)/9
otherwise, exptnl(level) = (level^4 + 55*level^2 - 56)/9

51 ≤ level:
exptnl(level) = floor(1.0548*exptnl(level-1))

Monster Book (credit to Chris from Kryptodev)
numCardsNeeded = (5 * MBLevel) * (MBLevel + 1)

Everything relating to HP/MP:
See LazyBui's Guide to HP and MP, no need to have info twice.

Base Accuracy:
Warriors/Magicians/Beginners = DEX * 0.8 + LUK * 0.5
Brawlers = DEX * 0.9 + LUK * 0.3
Bowmen/Thieves/Pirates/Gunslingers = DEX * 0.6 + LUK * 0.3

Base Avoid:
Warriors[/Magicians/Bowmen/Thieves/Beginners] = DEX * 0.25 + LUK * 0.5
Pirates = DEX * 0.25 + LUK * 0.5
Brawlers = DEX * 1.5 + LUK * 0.5
Gunslingers = DEX * 0.125 + LUK * 0.5

Hands = DEX + INT + LUK (used for Maker skill in KMS, thanks GW2000 for pointing that out)

Caps: (most of these are trivially common knowledge, but they're here for reference anyway)
Level: 200
HP/MP: 30000
STR/DEX/INT/LUK: 999
Weapon/magic attack/defense: 1999
Accuracy/avoid: 999
Meso: 2147483647 (or 2^31-1, the maximum value of a signed int)
Damage in one hit (normally): 199999

All of the above also apply to mobs, if the stat applies.

(non-thieves)
Min Miss Rate: 2%
Max Miss Rate: 80%
(thieves)
Min Miss Rate: 5%
Max Miss Rate: 95%

Cast times can be found in LazyBui's Attack Speed Reference

Base HP Recovery: 10 / 10 seconds while inactive
Base MP Recovery: 3 / 10 seconds

Mages' Improving MP Recovery skill: Character level * MP Recovery level / 10

EXP lost on death:
Warriors/Mages/Pirates' = (5 + 20 / Base LUK)%
Bowmen/Thieves' = (5 + 8 / Base LUK)%

Battleship Durability: Battleship level * 5000 + (Character level - 120) * 3000
Each point of durability is equivalent to 1 HP.

Energy Charge:
10000 units = 1 fully charged meter
Charge rate: Skill % * 100 units per monster per hit. In other words, at maximum level, it charges 192 units per monster per hit.
Energy Charge decay: 200 units / 10 seconds while inactive

AGF
blitzkrieg
Devil's Sunrise
Fiel
GameMX
Hidden-Street
JoeTang
KaidaTan
Kortestanov
LazyBui
RFSurg
Stereo
Sybaris
Truemark
ZakumSlaYers
50504724

Thank you!

This is for my own reference.

http://pastebin.com/UGt7uE66