When going camping, there are quite a bit of absolutely essential supplies that have to be taken along. The type and quantity of supplies required depends on the nature of the camping trip and the duration.
Tents are the extremely essential as places that provide sleep and shelter.
Sleeping bags are necessary, especially since it can get quite cold out in the wild. A sleeping pad or air mattress to place under your sleeping bag for cushioning purposes is also necessary.
If the place where the camp site is being set up violates campfires, then a portable stove to prepare food is necessary.
A flashlight (preferably with extra batteries) is also a must. Hatchets, saw, or ax to cut down wood either for a campfire (if they are permitted) or for other minor construction or repair purposes. Rope is also essential since it can be very useful.
Other essential camping equipment can mostly be bought from home. These include dishes, pots, pans, utensils, etc.
For serious backpackers and wilderness campers, the list given above is pretty much a basic one.
Here are some other absolute essentials to be bought on a camping trip:
A map in a watertight case, a compass (a GPS system will be even better), extra clothing, extra food and water, a first aid kit, and a knife.
Other supplies include matches (also in a water-tight container), a fire starter, sunglass and sunscreen (to protect your eyes and skin respectively), a method of water treatment (like a water filter, for example), a food storage device (for places where bears are common, a bear canister is an absolute must) and a whistle.
The whistle can be used in situations where you get stuck and wish to call out to somebody for help. The whistle will almost always last a lot longer than your vocal cords will.
All the above mentioned supplies will be quite useless if they are not used properly. The most essential of all camping supplies is knowledge and experience.