We started with the standards:
Tent, air mattress, sleeping bag, pillow. And then thought, We usually need a couple of extra tarps, one for under the tent and one for over if the rain fly wasn't enough to keep out inclement weather. Tools for setting up the tent(s), hammer, pliers, screw driver, extra rope or cord, and yes, duct tape!

The most success has come from those large plastic storage boxes that you can buy at K-Mart. We've labeled them as "kitchen", "cooking", "bath", and "camp". You can almost guess what's in each bin, but here's a breakdown in case you haven't thought of something:

Kitchen:
Frying pan(s), stew pot, teakettle, CAN OPENER, bottle opener, coffee pot, spatula(s), sharp knife, eating utensils, plates, roasting forks, matches (in a plastic bag), paper towels, pot holders, tin foil, plastic wrap, cutting board, small plastic dish tub, dish soap, dish towels, garbage bags with drawstrings, slop jar or can with a closing lid.

Cooking:
Salt and pepper, cooking oil/butter/margarine, ketchup, mustard, coffee/tea, onions, garlic, other spices. These are the bare bone essentials; think about what you will be cooking and bring that stuff too.

Bath:
Soap, toilet paper (especially if you are rustic camping), shampoo, towels, toilet and shaving articles, toothbrush and paste, comb and brush, sunscreen and bug repellents.

Camp:
Flashlight, fly swatter, first aid kit, sewing kit, string, clothes line, folding table, folding chairs, shovel, axe/saw, another tarp.

When you are packing your own gear, always take an extra pair of shoes and socks, a warm jacket and long pants.

You'll find other items that will enhance your camping experience, but without these essentials, you may never want to camp again.