While your list of supplies can vary greatly here is a list of some recommended items for camping (in alphabetical order):
Axe or hatchet to split wood and drive tent stakes
Backpack, hydration pack, or day pack for outings and hikes
Spare Batteries for flashlight, headlamp, and other devices
Camera or binoculars (optional but highly recommended)
Clothing appropriate for the location (sun, rain, snow, etc.) – pants, shirts, gloves, socks, etc.
Cookware including stove, pans, Dutch oven, utensils, plates, cups, and cutlery
Fire starters including two sources of fire, kindling, and starters
First Aid Kit in both your vehicle kit and hiking kit
Food, beverages, and cooler if bringing perishable food
Footwear such as hiking boots, sturdy shoes, socks
Illumination including a lantern, flashlight, or headlamp
Knife or multi-tool
Paracord or rope for securing a shelter, acting as a clothesline, etc.
Personal Items: insect repellent, sunscreen, toothbrush/paste, soap, toilet paper, towel, etc.
Rain Gear or poncho and hat (be prepared)
Saw (optional) to cut wood
Sleeping Bag or blankets to keep you warm at night
Sleeping Pad or cot for added comfort and to insulate you from the ground
Tarp used for added rain protection or as a footprint for your tent
Tent or other shelter (hammock, vehicle, tarp, or bivy)
Trash Bags for cleanup — remember to take nothing put pictures and leave nothing but footprints
Trowel or small shovel for sanitation in backcountry areas
Water Filter and water containers
Optional items include folding chairs, picnic blanket or mat, fishing poles, and entertainment items such as playing cards, Frisbees, kites, etc.