The full list on The Homebrewery
I'm a bit disappointed with beasts not being very much more than bags of hit points. And, yeah, a lot of creature types seem to have similar problems. But if I'm going to work on it, I'd rather start with some that impact players.

Evasive Leap. As a bonus action, the beast can move up to X feet without incurring attacks of opportunity.
Spoiler: Beasts with Evasive Leap
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Hare
Tiny beast, unaligned

Armor Class 11
Hit Points 1(1d4 - 1)
Speed 35ft.
STR DEX CON INT WIS CHA
6 (-2) 13 (+1) 8 (-1) 3 (-4) 10 (+0) 5 (-2)
Senses Passive Perception 10
Languages --
Challenge 0 (10 XP)
Evasive Leap As a bonus action, the hare can move up to 10 feet without incurring attacks of opportunity.

Keen Hearing. The weasel has advantage on Wisdom (Perception) checks that rely on hearing.

Actions
Kick. Melee Weapon Attack: +0 to hit, reach 5ft., one target. Hit 1 bludgeoning damage.

Otter
Small beast, unaligned

Armor Class 12 (Natural Armor)
Hit Points 7(2d6)
Speed 25ft., swim 30 ft.
STR DEX CON INT WIS CHA
9 (-1) 13 (+1) 10 (+0) 4 (-3) 13 (+1) 6 (-2)
Senses Passive Perception 11
Languages --
Challenge 1/8 (25 XP)
Evasive Leap. As a bonus action, the otter can move up to 5 feet without incurring attacks of opportunity.

Hold Breath. The otter can hold its breath for 15 minutes.

Actions
Bite. Melee Weapon Attack: +1 to hit, reach 5ft., one target. Hit 1 (1d4-1) piercing damage.

Hiss. As a bonus action, a target within 5 feet of the target must make a wisdom saving throw against a save DC of 13. On a failed save, the target is frightened of the beast until the end of its next turn.
Spoiler: Beasts with Hiss
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Goose
Small beast, unaligned

Armor Class 10
Hit Points 9(2d4 + 4)
Speed 30ft., swim 20 ft., fly 30ft.
STR DEX CON INT WIS CHA
12 (+1) 11 (+0) 14 (+2) 3 (-4) 11 (+0) 7 (-2)
Skills Intimidation +4
Senses Passive Perception 10
Languages --
Challenge 1/4 (50 XP)
Hiss. As a bonus action, a target within 5 feet of the target must make a wisdom saving throw against a save DC of 13. On a failed save, the target is frightened of the goose until the end of its next turn.

Actions
Beak. Melee Weapon Attack: +4 to hit, reach 5ft., one target. Hit 3 (1d4 + 1) piercing damage.

Snake
Tiny beast, unaligned

Armor Class 10
Hit Points 1(1d4 - 1)
Speed 20ft. swim 20ft.
STR DEX CON INT WIS CHA
2 (-4) 11 (+0) 8 (-1) 2 (-4) 13 (+1) 4 (-3)
Skills Intimidation +3
Senses Passive Perception 11
Languages --
Challenge 0 (10 XP)
Hiss. As a bonus action, a target within 5 feet of the target must make a DC 9 wisdom saving throw. On a failed save, the target is frightened of the snake until the end of its next turn.

Actions
Bite. Melee Weapon Attack: +0 to hit, reach 5ft., one target. Hit 1 piercing damage.

Keen Mind. The beast has advantage on Intelligence (Investigation) checks.
Spoiler: Beasts with Keen Mind
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Crow
Tiny Beast, unaligned

Armor Class 12
Hit Points 1(1d4 - 1)
Speed 10ft. fly 40ft.
STR DEX CON INT WIS CHA
2 (-4) 11 (+0) 8 (-1) 5 (-3) 12 (+1) 6 (-2)
Skills Investigation +3, Perception +3
Senses Passive Perception 13
Languages --
Challenge 0 (10 XP)
Keen Mind. The crow has advantage on Intelligence (Investigation) checks.

Actions
Beak. Melee Weapon Attack: +4 to hit, reach 5ft., one target. Hit 5 (1d6 + 2)

Note: This is based on Brayehn's crow, found here.

Fox
Small beast, unaligned

Armor Class 12
Hit Points 7(2d8 - 2)
Speed 30 ft.
STR DEX CON INT WIS CHA
10 (0) 14 (+2) 9 (-1) 5 (-3) 15 (+2) 8 (-1)
Skills Perception +3, Stealth +4
Senses Passive Perception 15
Languages --
Challenge 1/8 (25 XP)
Evasive Leap. As a bonus action, the fox can move up to 5 feet without incurring attacks of opportunity.

Keen Hearing and Mind. The fox has advantage on Wisdom (Perception) checks that rely on hearing and Intelligence (Investigation) checks.

Actions
Bite. Melee Weapon Attack: +2 to hit, reach 5ft., one target. Hit 4 (1d4 + 2) piercing damage.

Recoil. When hit with a melee attack from within 5 feet, the beast can deal X damage to the creature hitting it.

Weaker than multiattack, because it's only available as a reaction.
Spoiler: Beast with Recoil
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Giant Millipede
Medium beast, unaligned

Armor Class 13 (Natural Armor)
Hit Points 30(4d8 + 12)
Speed 20ft.
STR DEX CON INT WIS CHA
16 (+3) 8 (-1) 17 (+3) 1 (-5) 6 (-2) 3 (-4)
Senses Passive Perception 8
Languages --
Challenge 1 (200 XP)
Keen Smell. The giant millipede has advantage on Wisdom (Perception) checks that rely on smell.

Actions
Acid Slam. Melee Weapon Attack: +3 to hit, reach 5ft., one target. Hit 5 (1d4 + 3) bludgeoning damage and 5 (2d4) acid damage.

Reactions
Recoil. When hit with a melee attack from within 5 feet, the millipede can deal 5 (2d4) acid damage to the creature hitting it.

Porcupine
Small beast, unaligned

Armor Class 11 (Natural Armor)
Hit Points 16(3d6 + 3)
Speed 20 ft.
STR DEX CON INT WIS CHA
12 (+1) 8 (-1) 13 (+1) 2 (-4) 8 (-1) 3 (-4)
Senses Passive Perception 9
Languages --
Challenge 1/2 (100 XP)
Keen Smell. The weasel has advantage on Wisdom (Perception) checks that rely on smell.

Actions
Tail Swipe. Melee Weapon Attack: +3 to hit, reach 5ft., one target. Hit 4 (1d6 + 1) piercing damage.

Fire Quills.(Recharge 5-6) Ranged Weapon Attack: +1 to hit, reach 10ft., one target. Hit 2 (1d4 - 1) piercing damage.

Reactions
Recoil. When hit with a melee attack from within 5 feet, the porcupine can deal 2 (1d4) piercing damage to the creature hitting it.

Spitting Blind Attack Ranged Weapon Attack: +X to hit, reach 10 ft., one target. Hit: X damage, and target must succeed on a DC X Constitution saving throw or be blinded.
Spoiler: Beasts With Blinding Effects
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Archerfish
Small beast, annoying evil

Armor Class 11
Hit Points 7(2d4 + 2)
Speed 0ft., swim 30ft.
STR DEX CON INT WIS CHA
9 (-1) 12 (+1) 13 (+1) 2 (-4) 13 (+1) 4 (-3)
Skills Perception +4
Senses Passive Perception 14
Languages --
Challenge 1/4 (50 XP)
Water Breathing. The archerfish can breathe only underwater.

Actions
Bite. Melee Weapon Attack: +2 to hit, reach 5ft., one target. Hit 1 (1d4 - 1)

Water Shot.(Recharge 6) Ranged Weapon Attack: +2 to hit, reach 10 ft., one target outside water. Hit: 1 (1d4 - 1) bludgeoning damage, and target must succeed on a DC 5 Constitution saving throw or be blinded for one round.

Spitting Cobra
Small Beast, unaligned

Armor Class 13
Hit Points 19(3d4 + 3)
Speed 40ft., swim 30ft.
STR DEX CON INT WIS CHA
5 (-3) 16 (+3) 12 (+1) 2 (-4) 12 (+2) 6 (-2)
Skills Intimidation +5
Senses Blindsight 10 ft., Passive Perception 12
Languages --
Challenge 1 (200 XP)
Actions
Bite. Melee Weapon Attack: +4 to hit, reach 5 ft., one target. Hit: 2 (1d6 - 1) piercing damage plus 7 (3d4) poison damage.

Spit Venom.(Recharges after a Short or Long Rest) Ranged Weapon Attack: +6 to hit, reach 10 ft., one target. Hit: 7 (3d4) poison damage, and target must succeed on a DC 12 Constitution saving throw or be blinded for one minute.

Unending Stamina. While the beast is traveling, every two hours spent traveling count as only one hour for the purposes of determining exhaustion levels.

The intent is to represent creatures that spent most of their life traveling. I'm not sure it's phrased well, but the intent is to allow for sixteen hours of travel a day before needing to make any saving throws, and then two hours before making a constitution saving throw.
Spoiler: Beasts with Unending Stamina
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Albatross
Medium beast, unaligned

Armor Class 12
Hit Points 16(3d6 + 6)
Speed 10ft., 60 ft.
STR DEX CON INT WIS CHA
12 (+1) 15 (+2) 14 (+2) 4 (-3) 12 (+1) 5 (-2)
Skills: Acrobatics +3, Perception +4
Senses: Passive Perception 14
Languages: --
Challenge: 1/2 (50 XP)
Unending Stamina. While the Albatross is traveling, every two hours spent traveling count as only one hour for the purposes of determining exhaustion levels.

Keen Sight. The albatross has advantage on Wisdom (Perception) checks that rely on sight.

Actions
Wings. Melee Weapon Attack: +2 to hit, reach 5ft., one target. Hit 6 (2d4 + 1)

Antelope
Medium beast, unaligned

Armor Class 11
Hit Points 5(2d8 - 2)
Speed 40ft.
STR DEX CON INT WIS CHA
14 (+2) 13 (+1) 8 (-1) 3 (-4) 12 (+1) 5 (-3)
Senses Passive Perception 11
Languages --
Challenge 1/8 (25 XP)
Unending Stamina. While the Antelope is traveling, every two hours spent traveling count as only one hour for the purposes of determining exhaustion levels.

Actions
Hooves. Melee Weapon Attack: +2 to hit, reach 5 ft., one target. Hit: 4 (1d4 + 2) bludgeoning damage.