For Whitewater Kayaking:

Essentials:
Boat - Personal Flotation Device (PFD)
Helmet
Neoprene Spray Skirt
Quick drying clothing suitable to the conditions
Paddle
Safety Kit
Throw Bag
Boat Transportation Rack/Cartop Kit
Full water bottle or hydration system

Suggested:

Sunscreen
Whistle
Marine Radio or Cell Phone
Collapsible Spare Paddle
Flotation Bags
Dry Bag

For Touring/Sea Kayaking:
Essentials:
Boat - Personal Flotation Device (PFD)
Helmet (if paddling in surf)
Neoprene or Nylon Spray Skirt
Quick drying clothing suitable to the conditions
Paddle
Safety Kit
Full water bottle or hydration system

Suggested:

Sunscreen
Whistle
Marine Radio or Cell Phone
Collapsible Spare Paddle
Flotation Bags
Dry Bag

For Unknown Waters Add: Compass
Map Case with Regional Map
Book on Kayak Navigation

For Recreational Kayaking:
Essentials:
Boat - Personal Flotation Device (PFD)
Quick drying clothing suitable to the conditions
Paddle
Boat Transportation Rack/Cartop Kit
Full water bottle or hydration system

Suggested: 

Nylon Spray Skirt
Sunscreen
Whistle
Safety Kit
Bilge Pump
Marine Radio or Cell Phone
Collapsible Spare Paddle
Flotation Bags
Dry Bag