This list was created and kindly provided by user seeyaness. The original can be found here. It reflects LEO's current state as of writing this article. Potential future additions may not be reflected. This list is not intended to be exhaustive.

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[Armor]

Active
+5 Action Points

Agile
+1 Agility

Almost Unbreakable
Quadruples durability

Assassins
-15% damage taken from humans

Atomic Physicist
Fusion Cores last 25% longer

Attentive
+1 Perception

Auto Stim
Automatically use a Stimpak when hit while health is 25% or less, once every 60 seconds

Bolstering
Increased energy and damage resistance the lower your health, up to +35 at 10% health

Bulwark
50% reduced damage from explosions and magnitude of incoming staggers

Cavaliers
-15% damage taken while blocking or sprinting

Chameleon
20% Stealth Ability and become transparent while sneaking and not moving

Charistmatic
+1 Charisma

Cloaking
Being hit in melee generates a Stealth Field for 10 seconds, once per 60 seconds

Cryogenic
10% chance to freeze melee attackers and reduce their damage resistance by 25% for 10 seconds, once every 20 seconds

Cunning
+1 Agility and Perception

Duelists
25% chance to disarm attackers on a successful block

Endurance Runner
Infinite Action points out of combat

Exterminators
+50% Damage against Mirelurks and bugs

Fortifying
+1 Strength and Endurance

Fortunate
+1 Luck

Ghoul Slayers
+50% Damage against ghouls

Hazmat
+25 radiation resistance

Healthy
+5 Health

Hermits
-10% damage taken, +10% weapon damage, +30 Carry Weight and +10 Action Points
Only active when adventuring without a companion

Hunters
-15% damage taken from animals

Incendiary
30% chance to ignite melee attackers for 50 damage, once every 20 seconds

Low Weight
90% reduced weight

Lucky
+2 Luck

Martyrs
30% time dilation for 15 seconds during combat when at 20% or less health

Milk of Human Kindness
+2 Charisma and +1 Luck
Dont tell Strong about it

Mutant Slayers
-15% damage taken from Super Mutants

Nocturnal
Damage and Energy Resistance increase with the night
Up to +20 armor rating and energy resistance

Persevering
+1 Endurance

Piezonucleic Lining
+50% AP regen when taking Radiation Damage

Poisoners
+25 poison resistance

Powered
+5 Action Point Regeneration

Punishing
10% melee damage reflected back on attacker

Rad Powered
Grants +1 Strength per 133 rads, up to +7

Regenerating
Recover 1 health every 2 seconds while not in combat

Resistant
+5 Damage and Energy Resistance

Safecrackers
+100% Sweet-Spot Size while picking locks

Sharp
+1 Charisma and Intelligence

Smart
+1 Intelligence

Sneakers
Become 10% harder to detect while sneaking

Sprinters
+10% movement speed

Strong
+1 Strength

Tesla Coils
Deals 4 Energy Damage per second to nearby enemies

Titans
-15% damage taken while standing and not moving

Troubleshooters
-15% damage taken from robots

Unyielding
+3 to all stats when you are at 25% or less health

VATS Enhanced
-10% VATS Cost

Vanguards
Grants up to +35 Energy and Damage Resistance, the higher your health

Water Breathing
Enables you to breathe underwater

[Weapon]

Active
+10 Action Points

Angering
25% chance to frenzy your opponent on a successful block

Assassins
+50% Damage against humans

Bashers
Bashing damage increased by 40%

Berserkers
Increased Damage the lower your Resistance
+100% at 0 Resistance, -75% at 100+ Resistance

Blazing
25% chance to deal 50 Fire damage on a successful block

Bloodied
Increased damage the lower your health, up to +95% at 5% health

Cavaliers
-15% damage taken while blocking or sprinting

Charged
+10% chance to deal 100 Electrical damage on a successful block

Critically Acclaimed
15% Critical Hit Chance
Affected by crit damage bonuses

Deadeye
30% time dilation for 3 seconds while aiming down sights

Defiant
+100% Damage with the final shot in the magazine

Double
Double ammo capacity

Duelists
25% chance to disarm attackers on a successful block

Enraging
Critical Hits cause target to frenzy, stacking duration

Executioners
50 more damage when your target is below 40% health

Explosive
+15 Explosive Damage

Exterminators
+50% Damage against Mirelurks and bugs

Fast Hands
+50% Reload Speed

Freezing
+10 Cryo Damage (stackable)
Freeze targets and lower damage resistance by 25% for 10 seconds on Critical Hits (not stackable)

Frigid
20% chance to freeze and reduce damage resistance by 25% for 10 seconds when you block an attack

Furious
+15% damage after each consecutive hit on the same target

Ghoul Slayers
+50% Damage against ghouls

Hardy
+1 Endurance

Healthy
+10 Health

Hitmans
+10% damage while aiming down sights

Hunters
+50% Damage against animals

Incendiary
5 points of fire damage per second for 5 seconds, stacking damage

Instigating
+100% damage if the target is at full health

Irradiated
+50 Radiation Damage

Irradiating
50% chance to deal 50 Rads on a successful block

Jakobs
"If it took more than one shot"
+100% Ballistic Damage
-50% Mag Size

Junkies
+15% damage per withdrawal effect you are suffering

Kneecapper
20% chance to cripple the targets leg

Lightweight
90% reduced weight

Lucky Weapon
+100% Critical Damage, +15% critical meter recharge

Ma Li-Wans
"Is shooting bullets just not cool enough for you?"
+100% Energy Damage
-50% Cell Charge

Marksmans
+100% base range and 50% improved base accuracy and recoil

Medics
Heal targets for 10 health and 200 radiation

Mutant Slayers
+50% Damage against super mutans

Never Ending
Unlimited ammo capacity

Nimble
+75% movement speed while aiming down sights

Nocturnal
Increased damage at nighttime, up to +100%
Decreased damage at daytime, up to -66%

Overpowering
40% more power attack damage

Penetrating
30% penetration of damage and energy resistance

Plasma Infused
+10 energy damage
Can turn enemies into goo

Poisoners
+3 poison damage per second for 10 seconds, stacking damage

Powerful
+25% Damage

Protective
Take 40% less damage while power attacking

Quad
Quadruple ammo capacity
Stackable with other instances of the same effect

Quickdraw
-25% VATS Cost

Rapid
25% faster fire rate, 15% faster reload

Relentless
Refills your Action Points on a Critical Hit

Resilient
+150 damage resistance while reloading

Resolute
30% time dilation for 3 seconds when chambering the final round in the magazine

Riposting
Reflects 50% of melee damage back while blocking

Sentinels
-15% damage taken while standing and not moving

Staggering
+50% chance to stagger on hit with melee weapons, +30% with semi-auto guns, +5% with automatic guns

Stalkers
+100% VATS accuracy if not yet in combat
Double AP cost

Steadfast
+50 damage resistance while aiming

Suppressors
Reduce your targets damage output by 20% for 3s

Swift
+1 Agility

Troubleshooters
+50% Damage against robots

Two-Shot
Double projectile count
+100% Damage, +100% Recoil, +150% Spread

VATS Enhanced [Gun]
+33% VATS Accuracy, -25% VATS Cost
The latter is stackable, the former is not

VATS Enhanced [Melee]
-40% VATS Cost

Vampires
Grain brief health regeneration when you hit an enemy
+5 health over 2 seconds

Vigilant
+1 Perception

Vigorous
+1 Strength

Violent
+25% damage and limb damage, +200% recoil

Wounding
3 points of bleed damage per second for 5 seconds
Stacking unresistable/armor-penetrating damage