Here's a list of 50 commonly used carp rigs, each suited for different situations and bait presentations:

1. Hair Rig: A classic rig with the bait hair-rigged off the hook.
2. Bolt Rig: A fixed lead system that sets the hook when the carp takes the bait.
3. KD Rig: Features a unique hook arrangement for better hooking.
4. Blowback Rig: Uses a ring on the shank to improve hookholds.
5. Chod Rig: Designed for fishing over weed or debris.
6. Hinged Stiff Rig: Excellent for pop-ups and stiff presentations.
7. Multi Rig: Versatile and can be adjusted easily.
8. Zig Rig: For suspending bait at various depths.
9. Slip D Rig: Effective for bottom baits and pop-ups.
10. Ronnie Rig: Known for its aggressive hooking mechanism.
11. D Rig: Designed for presenting pop-ups and bottom baits.
12. Combi Rig: Combines a stiff boom with a supple hair section.
13. Running Rig: Allows the carp to run without feeling resistance.
14. Helicopter Rig: Good for long-range casting and tangle-free presentation.
15. Snowman Rig: Uses a bottom bait and a pop-up to create a balanced presentation.
16. 360 Rig: Allows the bait to rotate freely, increasing hook-ups.
17. German Rig: A variation of the blowback rig with a fixed ring.
18. Stiff Hinge Rig: Combines the hinged stiff rig with a supple boom.
19. Solid PVA Bag Rig: Ensures compact bait presentation.
20. Method Feeder Rig: Uses a method feeder to attract carp.
21. Inline Lead Rig: The lead is inline for better hook sets.
22. Lead Clip Rig: Allows the lead to be ejected if snagged.
23. Zig Float Rig: For presenting baits mid-water using a float.
24. Surface Rig: For fishing floating baits on the surface.
25. Adjustable Zig Rig: Allows adjustment of the bait depth without reeling in.
26. Banana Rig: Features a curved hook for better penetration.
27. Nash Fang Twister Rig: Known for its aggressive hook shape.
28. Slip D Rotator Rig: Uses a rotating D section for better hook holds.
29. Shocker Rig: Uses an elastic shocker to set the hook.
30. Spinner Rig: A rig that can spin around making it hard for the carp to eject.
31. Double Bottom Bait Rig: Uses two bottom baits for increased attraction.
32. Twin Rig: Presents two baits close together.
33. Elastic Hair Rig: Uses elastic on the hair for flexibility.
34. Heli-Safe Rig: A helicopter rig with a safety release system.
35. Wafter Rig: Balances the bait to just sink slowly.
36. Semi-Fixed Lead Rig: A hybrid of fixed and running lead setups.
37. Inline Bolt Rig: The lead sits inline with the hooklink.
38. Flat Pear Rig: Uses a flat pear-shaped lead.
39. Mag-aligner Rig: Uses a maggot and aligner for hooking.
40. Pineapple Rig: Flavored for attraction with pineapple scents.
41. Fake Corn Rig: Uses artificial corn as bait.
42. Critically Balanced Rig: Bait is balanced to sit just off the bottom.
43. Claw Rig: Uses a claw-shaped hook for better holding.
44. Tandem Rig: Uses two hooks in tandem.
45. Spring Rig: Incorporates a spring for extra movement.
46. Double Hair Rig: Features two hair-rigged baits.
47. Spod Rig: For casting large amounts of bait accurately.
48. Chod Helicopter Rig: Combines chod and helicopter principles.
49. Adjustable Hair Rig: Allows for easy hair length adjustments.
50. Floating Zig Rig: Uses buoyant material to suspend bait mid-water.

These rigs cover a wide range of carp fishing scenarios, from bottom fishing to surface and mid-water presentations. Each rig has its unique characteristics and advantages, making them suitable for different fishing conditions and bait types.