It depends, alot of schools/styles/systems claim "Shaolin" as part of it's lineage.
If you look at Bak Sil Lum (Northern Shaolin) you have 10 empty hand sets and a couple of supplemental ones.
1) Koy Moon (Opening the door)
2) Leng Low ( The Leader)
3) Jou Mah (The Sitting Horse)
4) Chum Sam (Striking the Heart)
5) Mo I (Martial Art)
6) Tun Da (The Short Strike)
7) Moi Fah (The Plum Flower)
8) Bot Bo (The Shuffling Step)
9) Lien Wan (Continuation)
10) Sik Fot (Skilled Technique)
Almost all Shaolin styles also have an "18 hand set" based on the original Darhma's teachings. Many also include "Tam Tui" in their curriculum, along with iron body and iron palm training and many other weapons sets.
Southern Shaolin, which includes Hung Gar has several sets which include,
1) Taming the Tiger (Kung Gee Fook Fu Kuen)
2) Tiger/Crane (Fu Hok Seung Yin)
3) 5 Animals/5 Elements (also called 10 shaped fist; Sup Ying Kuen)
4) Iron Wire/Thread (Tiet Sin Kuen)
5) 5 Animals (sames as previous, without the inclusion of the elements)
6) 4 Gates Sparring
7) Lau Gar Kuen
The first four sets listed are the "pillar" sets of Hung Gar. This also includes some supplemental training and weapons sets. Also, some lineages include other sets as well.
There is also Ha Say Fu Hung Gar that has 5 different animal sets, and is also thought to be an older branch of Hung Gar from Canton, although there isn't much documentation on it's actual lineage.
1) Panther
2) Tiger
3) Crane
4) Snake
5) Dragon
Some styles like Choy Li Fut also have a "5 animals set" in it's curriculum (it has over 190 sets in it)
Hsing-Yi has 12 animals in it's curriculum, those include...
1) Dragon
2) Tiger
3) Monkey
4) Horse
5) Alligator
6) Fighting Chicken
7) Falcon
8) Snake
9) Swallow
10) Roc (mythical bird)
11) Eagle
12) Bear
Then there are also the animal styles of kung fu that are on their own, and to name a few...
Praying Mantis (southern, northern, 7-star)
Eagle Claw
Tiger
Dragon