There are at least 16 you need to know that use various parts of the body, but above are the nine simplest fists. Here's one list of all 16, but there are always differences and stuff, and they go with different movements (rising, falling, forward, back) as well as fitting certain specific parts of the body or types of attack.

1. Kikaku-ken (aka Zutski) Head-butt

2. Fudo-ken (aka Nio-ken or Kongo-ken) "Immovable (clenched) fist"

3. Shikan-ken '4-Rings Fist'

4. Boshi-ken (aka Shito-ken) Thumb-drive fist (refers to the piercing end a blade)

5. Shako-ken Palm-strike/claw-hand fist

6. Kiten-ken (aka Shuto) Knife-hand

7. Shitan-ken Finger-spear/thumb-pressure grip

8. Happa-ken "8 Leaves" Open-hand (slap)

9. Koppo-ken "Bone method fist" Thumb-knuckle fist

10. Shishin-ken "Finger-needle" fist

11. Shuki-ken 'Elbow-gun' (Elbow and forearm)

12. Sokki-ken Knee and shin

13. Sokuyaku-ken Heel of foot

14. Sokugyaku-ken Ball-of-foot & toes

15. Shizen-ken "Natural weapons" (teeth, whatever, basically, anything not on the list!)

16. Taiken "Body-as-weapon"

(and here's a video)