On wizardingworld.com (formerly known as Pottermore), there are 140 possible patronus forms you can conjure if you take their patronus quiz. One of these may be yours! That being said, there are some missing which probably should be included. I've listed those here as well. Not every possible patronus form has been added to this list, however, because that would be impossible! 

Images of each of Wizarding World's Patronus Forms can be found at:

https://harrypotter.fandom.com/wiki/Patronus_Charm 

According to wizardingworld.com, here are the top 20 most common patronuses:

1. Dolphin

2. Tonkinese Cat

3. Manx Cat

4. Nebelung Cat

5. Fox

6. St Bernard Dog

7. Weasel

8. Bassett Hound

9. Black And White Cat

10. Hedgehog

11. Deerhound

12. West Highland Terrier

13. Siberian Cat

14. Tortoiseshell Cat

15. White Stallion

16. White Mare

17. White Swan

18. Osprey

19. Borzoi

20. Ragdoll Cat

According to Reddit and other sites, these are the patronuses Wizarding World considers “Unusual” and “Very Rare.”

Unusual:

1. Bat

2. Black Bear

3. Brown Owl

4. Buffalo

5. Cheetah

6. Doe

7. Eagle Owl

8. Elephant

9. Great Grey Owl

10. Hyena

11. Impala

12. King Cobra

13. Leopard

14. Leopardess

15. Lion

16. Lioness

17. Little Owl

18. Lynx

19. Orca

20. Oryx

21. Peacock

22. Polar Bear

23. Python

24. Raven

25. Rhinoceros

26. Scops Owl

27. Seal Shark

28. Snowy Owl

29. Stag

30. Tiger

31. Tigress

32. Vulture

Very Rare:

1. Abraxan Winged Horse

2. Dragon

3. Erumpent

4. Fire-dwelling Salamander

5. Granian Winged Horse

6. Hippogryff

7. Occamy

8. Runespoor

9. Thestral

10. Unicorn

Patronus List, supplied from Wizarding World:

Associated with Water:

1. Black Swan

2. Dolphin

3. Heron

4. Orca

5. Salmon

6. Seal

7. Shark

8. White Swan

Not included on Wizarding World:

1. Albatross

2. Alligator

3. Crab

4. Crocodile

5. Duck

6. Frog

7. Goose

8. Penguin

9. Scorpion

10. Turtle

Bears:

1. Black Bear

2. Brown Bear

3. Polar Bear

Not included on Wizarding World:

1. Panda Bear

Birds:

1. Blackbird

2. Buzzard

3. Crow

4. Eagle

5. Falcon

6. Goshawk

7. Hawk 

8. Hummingbird

9. Kingfisher

10. Macaw

11. Magpie

12. Marsh Harrier

13. Nightjar

14. Osprey

15. Ostrich

16. Peacock

17. Pheasant

18. Pine Marten

19. Raven

20. Robin

21. Rooster

22. Sparrow

23. Sparrowhawk

24. Swallow

25. Swift

26. Vulture

Not included on Wizarding World:

1. Bluebird

2. Bluejay

3. Dove

4. Hawk

5. Rooster

Big Cats: 

1. Cheetah

2. Impala

3. Leopard

4. Leopardess

5. Lion

6. Lioness

7. Lynx

8. Tiger

9. Tigress

10. Wildcat

Deer:

1. Doe

2. Stag

Dogs:

1. Basset Hound

2. Beagle

3. Bloodhound

4. Borzoi

5. Chow Dow

6. Deerhound

7. Fox

8. Fox Terrier

9. Greyhound

10. Husky

11. Ibizan Hound

12. Irish Wolfhound

13. Mastiff Dog

14. Mongrel Dog

15. Newfoundland

16. Rottweiler

17. St. Bernard

18. West Highland Terrier

19. Wolf

Not included on Wizarding World:

too many to list.......

Domesticated Cats:

1. Black and White Cat

2. Calico Cat

3. Ginger Cat

4. Manx Cat

5. Nebelung Cat

6. Ocicat

7. Ragdoll Cat

8. Russian Blue Cat

9. Siberian Cat

10. Sphynx Cat

11. Tonkinese Cat

12. Tortoiseshell Cat

Not included on Wizarding World:

1. Persian Cat

2. Tabby Cat

Horses:

1. Bay Mare

2. Bay Stallion

3. Black Mare

4. Black Stallion

5. Chestnut Mare

6. Chestnut Stallion

7. Dapple Grey Mare

8. Dapple Grey Stallion

9. Dun Mare

10. Dun Stallion

11. Piebald Mare

12. Piebald Stallion

13. White Mare

14. White Stallion

Not included on Wizarding World:

1. Mustang

Magical:

1. Abraxan Winged Horse

2. Dragon

3. Erumpent

4. Fire-dwelling Salamander

5. Granian Winged Horse

6. Hippogryff

7. Occamy

8. Runespoor

9. Thestral

10. Unicorn

Not included on Wizarding World:

1. Griffin

2. Phoenix

Monkeys/Apes:

1. Capuchin Monkey

2. Orangutan

Not included on Wizarding World:

1. Ape

2. Gorilla

3. Monkey

Owls:

1. Brown Owl

2. Great Grey Owl

3. Eagle Owl

4. Little Owl

5. Scops Owl

6. Snowy Owl

Not included on Wizarding World:

1. Barn Owl

2. Screech Owl

Rabbits/Hares:

1. Brown Hare

2. Mountain Hare

Not included on Wizarding World:

1. Hare

2. Jackrabbit

3. Rabbit

Rodents: 

1. Field Mouse

2. Grey Squirrel

3. Red Squirrel

4. Vole

5. Woodmouse

Not included on Wizarding World:

1. Beaver

2. Chinchilla

3. Chipmunk

4. Guinea Pig

5. Rat

Snakes:

1. Adder

2. Black Mamba

3. Grass Snake

4. King Cobra

5. Python

6. Rattlesnake

Not listed on Wizarding World:

too many to list........

Weasels:

1. Badger

2. Mink

3. Otter

4. Polecat

5. Stoat

6. Weasel

Not listed on Wizarding World:

1. Ermine

2. Ferret

3. Mink

4. River Otter

5. Sea Otter

6. Wolverine

Also Included on Wizarding World:

1. Aardvark

2. Bat

3. Buffalo

4. Dragonfly

5. Hedgehog

6. Mole 

7. Rhinoceros

8. Shrew

9. Wild Boar

Also not included on Wizarding World:

1. Butterfly

2. Camel

3. Coyote

4. Giraffe

5. Goat

6. Kangaroo

7. Porcupine

8. Ram

9. Sheep

10. Spider

11. Wombat

12. Zebra

Sources:

https://www.wizardingworld.com/features/what-your-patronus-says-about-you 

https://www.reddit.com/r/harrypotter/comments/54hjcv/the_complete_pottermore_patronus_quiz_breakdown/