The following is a crash-course on introducing new fantastic wildlife into your game with ease. You don't HAVE to use the monster creation process described in the DMG. All you need is the DMG and a little creativity!
Chomp Hopper
Statblock: Frog
Customization: Replace ranged tongue attack with a +3 to hit 1d8 piercing bite attack.
Customization: Replace ranged tongue attack with a +3 to hit 1d8 piercing bite attack.
Sea Grappler
Statblock: Dolphin
Customization: Keen hearing. Also, descriptively it has the ability to grapple, and also to hold and manipulate objects.
Fuzzflit
Statblock: Rat
Customization: 60ft flying speed.
Tasked Octopus
Statblock: Giant Octopus
Sky Wolf
Statblock: Hawk
Customization: Give it the wolf's or mastiff's grappling bite attack.
Guardian Wolf
Statblock: Wolf
Customization: Give it the elk's ram attack.
Beak Strider
Statblock: Elk
Customization: Give it the eagle's keen sight.
Sky Shark
Statblock: Giant Eagle
Customization: Replace beak with the reef shark's bite attack.
Gerwonda
Statblock: Giant Ape
Customization: Give it the lion's bite attack. Change type to monstrosity.
Gulper
Statblock: Rhinoceros
Customization: Remove the charge trait and the gore attack. Give it the giant frog's swallow ability with a size limit of medium.
Vretcher
Statblock: Quipper
Customization: Give it the frog's speed stats, amphibious, and standing leap.
Raptor Hound
Statblock: Mastiff
Shark Bear
Statblock: Black Bear
Customization: Give it the reef shark's bite attack.
Warrior Elephant
Statblock: Elephant
Customization: Treat it as wearing plate armor.
Dazzlecat
Statblock: Cat
Customization: Increase its charisma to 15. Change type to monstrosity.
Dangling Trapper
Statblock: Poisonous Snake
Customization: Replace poison damage with grapple condition.
Rhaspion
Statblock: Deer
Customization: Give it the panther's bite attack and pounce trait.
Battle Bird
Statblock: Eagle
Customization: Give it the tiger's bite attack.
Terror Horse
Statblock: Horse
Customization: Give it the wolf's bite attack.
Domestic Egg Goat
Statblock: Goat
Customization: Remove charge trait.
Eastern Owlbear
Statblock: Owlbear
Mercat
Statblock: Cat
Customization: Give it 40ft swim speed, halve its land speed.
Tangle Lizard
Statblock: Lizard
Customization: Give its bite attack a DC 11 DEX save vs. Grapple.
Beak Lizard
Statblock: Lizard
Customization: increase its damage to 2.
Dazzlephant
Statblock: Elephant
Customization: Increase its charisma to 15.
Sea Biter
Statblock: Seahorse
Customization: Give it a 1d4 piercing damage bite attack with +2 to hit.
Owl Racoon
Statblock: Giant Rat
Mountain Herd Dog
Statblock: Camel
Customization: Give it a wolf's bite attack.
Beak Cat
Statblock: Tiger
Customization: replace the bite with an axe beak's beak attack.
Reft Horse
Statblock: Horse
Customization: +10ft speed.
Poison Dart Zebra
Statblock: Horse
Customization: Custom trait. Poison Spines: When a creature makes a melee weapon attack against this creature, they must make a DC 11 DEX save or take 1d4 poison damage and become poisoned.
Bleat Bat
Statblock: Bat
Customization: Give it the charge trait.
Psionephant
Statblock: Elephant
Customization: Remove all traits relating to the tusks and trunk. Give it psionics-like spells to cast at-will.
Rotten Polecat
Statblock: Weasel
Customization: It can cast stinking cloud 3 times a day.
Tangle Cat
Statblock: Cat
Customization: It can grapple things with its tail.
Wander Goat
Statblock: Goat
The Great Ancestral Fish
Statblock: Lizard
Customization: Give it 50ft swimming speed.
Pack Monkey
Statblock: Ape
Customization: Give it the mastiff's grappling bite attack.
Hell Whale
Statblock: Killer Whale
Customization: Give its attack an additional DC 11 STR save vs. Grapple.
Choke Rot
Statblock: Octopus
Customization: Change type to plant. Reduce all speed to 0.
Bob-dog
Statblock: Mastiff
Customization: Remove the grapple save from its bite attack.
Flying Snapper
Statblock: Eagle
Customization: Give it the crocodile's bite attack.
The Killer Rabbit
Statblock: Giant Frog
Customization: Replace reach attack with the dimetrodon's bite attack. Give the bite attack a DC 11 save vs. Grapple. Remove swallow.
Auqckwoard
Statblock: Goat
Customization: 30ft fly speed, remove charge trait. Replace ram with giant eagle's beak attack.
Gore Beast
Statblock: Elephant
Gluttonodon
Statblock: Rhinoceros
Customization: Remove charge and gore attack. Give it the crocodile's bite attack.
Watcher in the Trees
Statblock: Giant Rat
Customization: 30ft climbing speed
Hunter Cow
Statblock: Aurochs
Customization: Give it the tiger's bite attack.
Sky Sloth
Statblock: Giant Rat
Custimization: Reduce speed to 5ft. 20ft flying speed. Remove all attacks.
Pink Rat Trap
Statblock: Cat
Manbear
Statblock: Black Bear
Customization: Speaks bestial.
Dodrio
Statblock: Axe Beak
Customization: Multiattack. When this creature uses the attack action, it makes 3 attacks.
Slithe
Statblock: Deer
Customization: Give it the giant poisonous snake's poison bite attack.
Land Gull
Statblock: Goat
Customization: Remove charge trait and ram attack. Give it the giant eagle's beak attack.
Great Centauroid
Statblock: Centaur
Customization: Increase size to huge.
Land Shark
Statblock: Horse
Customization: Give it the reef shark's bite attack.
Basher Monkey
Statblock: Ape
Customization: Give it the goat's ram attack and the charge trait.
Ick
Statblock: Cat
Customization: Give it the ranged tongue attack and swallow attack of the giant frog, limited to tiny targets.
Tiny Terror
Statblock: Rat
Customization: Give it 40ft speed and 40ft climbing speed. Give it the tiger's bite attack.
Crawling Bat
Statblock: Giant Rat
Customization: Give it 40ft flying speed and the bat's senses.
Rexodon
Statblock: Rhinoceros
Customization: Remove the charge and gore trait and attack. Give it the giant eagle's beak attack.
Crowned Lion
Statblock: Lion
Customization: Give it the giant goat's charge and ram.
Sea Dazzler
Statblock: Reef Shark
Customization: Remove all attacks. Increase its charisma to 15.
Beakdog
Statblock: Wolf
Customization: Replace bite attack with axe beak's beak attack.
Trophy Horse
Statblock: Horse
Customization: Given it the axe beak's beak attack.
Walking Maw
Statblock: Black Bear
Customization: Give it the crocodile's bite attack.
Venom Dog
Statblock: Mastiff
Customization: Give it the giant poisonous snake's poisonous bite attack.
Dashram
Statblock: Rhinoceros
Lumbering Grazer
Statblock: Black Bear
Customization: Replace its bite attack with a giant elk's charge and ram.