The most updated list of modifications/abilities is in the resource section. It includes combat maneuvers from the battlemaster fighter.
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1 Action Surge (Fighter) Add one additional action and bonus action 1/short rest
2 Advantage on Save or Saves
3 Aggressive (Orc) As a bonus action move up to creature's speed toward an opponent.
4 Anti-Magic Cone/Aura (Beholder) Magic does not function within the cone/aura.
5 Arcane Ward (Abjuration Wizard) Arcane ward absorbs 10, 15, 20, 25 - casting spells recharges it 2 pts./spell lev.
6 Assassinate (Rogue) Advantage vs. creature it surprises and any hit is an auto crit.
7 Attribute Drain (Shadow) On a hit, reduce strength (or other ability) by 1d4. Target dies if reduced to 0 in attribute.
8 Aura of Courage (Paladin) Allies within 10' cannot be frightened (20'/30' version for higher levels)
9 Aura of Fire, Cold, Necrotic, etc. (Lich) Damage to those within 5'/10' 1d8/2d8/3d8/4d8
10 Aura of Protection (Paladin) Allies within 10' gain +CHAR bonus to saves 20'/30' version too
11 Bardic Inspiration (Bonus Action) Grant 1d8 die that can be used within 1 min. 2/rest
12 Battlemaster Combat Maneuver (pick 3) See options in PHB
13 Benign Transposition (Conjuration Wizard) Teleport within 30' or switch places with a willing target within range 2/rest
14 Better Armor Add 2, 3, 4, 5 to AC
15 Blindsense (Grimlock) 30' range
16 Blood Frenzy (Sahuagin) Advantage to attack any creature that doesn't have all its hit points.
17 Bonus to Attack Damage (5, 10) Extra damage +5/+10 version
18 Breath Weapon (Dragon) 30' cone 3d6, 5d6, 7d6, 9d6, etc.
19 Cantrip user choose 3 or 4
20 Chameleon Skin (Troglodyte) Advantage to Dexterity Hide checks
21 Charger (Feat) Dash and 1 attack or shove. If moved more than 10' add +5 to damage
22 Class Levels or Spellcaster See PHB for details
23 Cloak of Shadows (Shadow Monk) In dim light or darkness, use your action to become invisible.
24 Cunning Action (Rogue)/Step of the Wind (Monk) Disengage, Dash, Hide, or Use Item as a bonus action (Step of the Wind: disengage or dash, and jump distance x2 for turn)
25 Cutting Words (Bard) Apply 1d8 negative to creature d20 roll within 60' as a reaction (2/rest)
26 Damage Absorption (Flesh Golem) Instead of taking damage, regenerate from that damage (choose type)
27 Damage Transfer (Darkmantle) Transfer 1/2 damage taken on a hit to linked creature grappled or within 20' (Charisma DC 13 to establish ranged link - bonus action)
28 Dark One's Blessing (Warlock) When creature is reduced to 0 hp by your spell or melee attack, gain 5, 10, 15, 20 hp)
29 Dark One's Luck (Warlock) Add 1d10 to a abilty check or save - 1/rest (Possibly add to attack as well)
30 Death Burst (Magmin) Damage in a burst 10' radius 3d6, 4d6, 5d6, etc.
31 Death Wail (Banshee) Creatures within 30' make DC 13 Con Save; on fail, drop to 0 hp. On success, take 3d6 psychic damage
32 Deflect Missiles (Monk) Use reaction to block/catch a missile - 1d10+dex+level to negate damage.
33 Entropic Ward (Warlock) Impose disadvantage vs. one attack. If it misses, your next attack gains advantage 1/rest
34 Ethereal/Phase (Bonus Action) Shift into or out of phase (like a phase spider)
35 Evasion (Rogue/Monk) When creature makes a DEX save to avoid damage, creature takes 0 damage on save, 1/2 on failure.
36 Extra Attack (Flurry of Blows too) Take an extra attack per round
37 Fey Presence (Warlock) Wis save vs. Spellcasting DC - cause each creature within 10' cube from subject to be charmed 1/rest
38 Fighting Style, Archery add 2 to hit with bows
39 Fighting Style, Dueling add 2 to damage with one handed weapon
40 Fighting Style, Protection as a reaction impose disadvantage vs. one attack against ally within 5'
41 Flyby Attack (Peryton)/Mobile (Feat) Do not take AO vs. creature attacked this round. Add 10 to speed
42 Frightful Presence/Fear Aura (Dragon) DC 19 wisdom save or be frightened (all within 20' - 120' for dragon like creatures)
43 Gaze (Petrify, Damage, Death, etc.) As an action (recharge 5-6) CON Save DC 14
44 Grapple/Constrict (Constrictor Snake) On successful grapple, deliver 3d6 damage per round until grapple broken or escaped
45 Guided Strike (Cleric, War 2/day) add 10 to hit (bonus action)
46 Hide in Plain Sight (Ranger) Ability to hide without cover
47 Holy/Unholy Strike (extra damage) 3d6 addition damage or more
48 Hunter's Mark (Ranger) mark quarry gain 1d6 to hit and 1d6 on incite, perception, survival to track vs. that creature
49 Hypnotic Gaze (Enchantment Wizard) vs. 1 creature within 5' Wis save vs spellcasting DC for charm
50 Immunity (choose) Immune to specific energy attack or non-magical weapons
51 Incorporal (Undead) Damage resistance to all but magical weapons
52 Inspiring Leader (Feat) Up to 6 friendlies within 30' who can see and gain temp hp level+Cha bonus (make an action not 10 min.)
53 Lay On Hands (Paladin) Creature can touch to heal like Paladin - 5/CR, use 5 to cure disease or poison condition
54 Leadership (Hobgoblin Captain) Friendlies within 30' gain d4 to attack or save. 1/rest
55 Legendary Resistance If creature fails a save, it can choose to succeed instead 3/day
56 Life Drain (Wraith) Damage lowers maximum hit points until rest. Death at 0 hp.
57 Lucky (Feat) 3/day re-roll a d20 for or against
58 Mage Slayer (Feat) Creature within 5' casts, make a reaction attack. Give Disad for Concentration. Gain advantage vs. spells of caster within 5'.
59 Magic Resistance (Balor) Advantage vs. spell saves
60 Martial Advantage (Hobgoblin) add 2d6 to hit when ally within 5' of target
61 Max Hit Points or More Hit Points
62 Mind Blast (Mind Flayer) 60' cone; DC 15 INT save 4d8+4 damage and stunned for 1 minute (repeat save at end of turn) (Recharge 5-6)
63 Otherworldly Perception (Kuo-Toa)/Alert (Feat) Can sense presence of creature within 30' -- +5 to initiative, can't be surprised, others don't gain advantage vs you when hidden
64 Pack Tactics (Kobold) advantage to attack creature if it is within 5' of an ally
65 Paralysis (Ghoul) Make a DC 13 con save on hit or be paralyzed - re-save at the end of each turn
66 Parry (Marilith) As a reaction, add 5 to AC vs 1 melee attach you can see
67 Patient Defense (Monk) Take dodge action as a bonus action 2/rest
68 Possession (Ghost) DC 13 charisma save or be posessed. Possession lasts until body drops to 0 hp or entity is turned and driven from body
69 Pounce (Lion) If you move at least 20' and hit with claws, DC 13 Strength Save or target prone and gain a bite bonus attack.
70 Projected Ward (Abjuration Wizard) Arcane ward absorbs 10, 15, 20, 25 - casting spells recharges it 2 pts./spell lev.that can protect an ally within 30'
71 Rage (Barbarian) Gain resistance vs. non-magical weapon damage - and adv.on strength checks and +2 damage - 1 min. 1/rest
72 Rampage (Gnoll) When reducing foe to 0 hp, run up to 1/2 speed and make another attack
73 Read Thoughts (Doppelganger) read surface thoughts w/in 60' Gain advtg on Wisdom (insight), Charisma (Deception, Intimidation, Persuasion) checks vs target
74 Reckless Attack (Minotaur) gain advantage on attacks, but also grant advantage on attacks against
75 Regeneration (Troll) At the start of each turn, gain 10, 20, 30 hp unless fire or acid damage taken that turn/ Oni version regen all damage while >1 hp
76 Rope and Reel (Roper) make an attack with rope/lasso, whip, or tentacle and then drag Strength Contest to drag 15'
77 Second Wind (Fighter) 1d10+level hp gained 1/rest
78 Sentinal (Feat) AO vs. creature stops its movement - you gain AO even vs. disengaging foes - if creature within 5' makes attack vs. other, you gain AO.
79 Shadow Arts (Shadow Monk) cast darkness, darkvision, pass without trace or silence 2/rest
80 Shadow Step (Shadow Monk) bonus action in dim light or darkness to teleport up to 60', then you have advantage on first melee attack you make.
81 Shapechanger (Werebeast, Druid)
82 Siege Monster (Earth Elemental) For huge or larger creatures…attack does 2x damage to objects and structures
83 Slippery (Kuo-Toa) Advantage on ability checks or saves vs. grapple
84 Spider Climb (Ettercap) can climb up surfaces or on ceilings without making any checks
85 Standing Leap (Bullywug) Leap up to 20' standing
86 Steadfast (Bearded Devil) Can't be frightened while it can see an ally within 30'
87 Stench (Troglodyte) Any within 5' make DC 12 Con save or be poisoned until creature's next turn. Save grants immune for 1 hour
88 Stunning Strike (Monk) Hit target must succeed on a CON save or be stunned until the end of your next turn (DC 8 + prof.+ wis)
89 Superior Invisiblity (Faerie Dragon) Become invisible and remain that way even when attacking.
90 Sure-Footed (Dao) Advantage on Strength and Dexterity saves against getting knocked prone.
91 Surprise Attack (Sneak Attack) When surprise, or when ally within 5' of target, gain 2d6, 3d6, 4d6, 5d6 to damage.
92 Sweeping Tail Attack Tail targets all within 15' swipe in one direction. +6 to hit (1d6+2/2d6+3/3d6+4/4d6+5)DC 13 STR or knocked prone/pushed 10'
93 Teleport (Balor) Teleport up to 120'
94 Tunneler (Umber Hulk) Can burrow through solid rock at 1/2 burrowing speed. (5' wide, 8' high tunnel)
95 Turn Immunity (Revenant) Can't be turned
96 Turn Resistance (Lich) Advantage vs. turn attempts
97 Uncany Dodge (Rogue) Use reaction to take 1/2 damage from an attack that hits from source you can see
98 Undead Fortitude (Zombie) When reduced to 0 hp, roll CON Save DC 5+ damage taken, unless the damage is radiant or crit hit; success keeps you at 1 hp
99 Warding Flare (Cleric, Light) As a reaction impose disadvantage vs. one attack from creature within 30'…3/day
100 Web, Web Sense, Web Walker (Giant Spider) Attack: +5 to hit - 30/60 ft. target restrained DC 12 Strength to escape - or create sticky web 20'x20' (Recharge 5-6)
Other Options
Devil's Sight 120' darkvision that can even see in magical darkness
Displacement (Displacer Beast) Attacks vs. creature are at disadvantage, but if hit, the effect is disrupted until the end of its next turn.
Earth Glide (Earth Elemental) Creature can move through earth and stone without disturbing the earth or stone.
Faultless Tracker (Invisible Stalker) Creature knows direction and distance to quarry as long as they are on the same plane.
Fighting Style, Two-Weapon Fighting Make an off hand attack and add strength/dex modifier to damage on off hand attack
Ground Shaking Smash Force DEX save to all within 5' - failure does 2d6 damage, save 1/2 damage.
Hurl Flame, Ice, Energy, etc. Attack range 150': +6 to hit; 4d6 damage
Inspiration Can roll any single attack, save or check at advantage (some creatures have 2 or 3 uses)
Luring Song (Harpy) DC 11 Wisdom save within 300' or be charmed and lured toward song; must dash toward sound, can make a new save if threat
Mimicry (Hag) Mimic animal noises and human voices DC 14 wisdom (insight) to detect as false
Misty Escape (Warlock) Teleport up to 60' 1/rest
Nature's Wrath Spectral vines sprin up within 10' of you. STR or DEX save or creatures restrained. Repeat save at end of each creature's turn.
Portent Roll 2 d20 and you can replace any roll for or against with one. Recharge each day.
Potent Cantrip Even misses do 1/2 damage.
Rejuvination (Flame Skull) If killed or destroyed, regain all hp in 1 hour unless holy water sprinkled on remains, or dispel magic or remove curse is cast.
Sculpt Spells Omit 1 plus spell level chosen creatures from damage of AoE spell cast.
Spell Immunity (Helmed Horror) Creature is immune to 3 spells, typically fireball, heat metal and lightning bolt
Stomp and Pin Attack deals 1d6/2d6/4d6/6d6 (depending on size) and target is prone and pinned (restrained).
Swallow (Behir) vs. Medium or smaller - swallow, blinded and restrained, total cover vs. attacks and efects, takes 6d6 acid damage each turn
Vampric Attack Gain back 1/2 damage dealt with a single attack
Wild Magic 5% chance that Wild Magic Surge happens when using spell or spell like ability.
Combat Maneuvers (Battlemaster Fighter)
Commander's Strike Forgo one attack, comanding an ally to attack instead (bonus action) - add d8 damage.
Disarming Attack On hit, foe makes STR save to avoid dropping weapon/item - add d8 damage.
Distracting Strike On hit, ally gains advantage vs. target on next attack in same round - add d8 damage.
Evasive Footwork Add d8 to your AC as you move this turn.
Feinting Attack Bonus action to feint vs. melee foe, gain advantage on next attack and add d8 damage.
Goading Attack On hit, force WIS save or foe gains disadvantage to attack any other than you until end of your next turn.
Lunging Attack Increase your reach by 5 feet - add d8 damage.
Maneuvering Attack On hit, move an ally into a better position (moving 1/2 speed) - add d8 damage.
Menacing Attack On hit, force WIS save to resist being frightened - add d8 damage.
Precision Attack Add d8 to your attack roll.
Pushing Attack On hit, force STR save to resist being pushed 15' - add d8 damage.
Rally Bonus action to boost resolve to add d8+CHA bonus temp hit points to an ally you can see or hear.
Riposte When a creature misses you, use a reaction to attack - add d8 damage.
Sweeping Attack On a hit, you can add d8 damage to an adjacent foe if the to hit score would have scored a hit on that creature.
Trip Attack On a hit, force STR save to resist being tripped - add d8 to damage.
