Pot grippers are sometimes sold with cook sets and these work great for lifting the hot pots or pans off the stove. But if you want a utensil that works two jobs, bring a pair of pliers. These work fine as pot grips and if you ever have to fix a piece of your gear, you have a tool for it.
A standard stainless steel or titanium nesting pot set (with a smaller pot nesting inside the larger one) is perfect. You don't need more than this on a short trip. This is what you will use to boil all of your water in and to cook most of your meals.
Utensils made out of a lightweight, heat resistant material such as lexan work well for camp cooking. Most backpackers get by using only a spoon to stir and eat with, but if you don't mind carrying extra utensils then a fork and knife can be brought as well. A mini spatula made out of lexan or stainless steel is good to bring if you are going to be baking or cooking things like hash browns in the morning.
A lightweight nonstick fry pan is an amazing cooking tool in camp if you want to make such creations such as pizza, calzones, hash browns, sticky buns or bread on a long expedition. It can be used upside down as a surface to roll dough out on with a water bottle for a rolling pin.
A dromedary water bag works as a makeshift sink in the backcountry. This folds to a small size when it is not filled, and it holds an ample amount of water. Use these to collect water for boiling and cooking and hang them from a branch to rinse to create a stream of water to rinse off your hands and face.
A small handheld strainer works as a sieve for straining out large floaters in your drinking water, as well as when you are doing the dishes. You may want to dump out the water you have used for washing, but you don't want to dump all of the large food particles that you need to pack out.
Stove and Stove Repair Kit
Your stove of course is one of the most important items, and no matter what kind you choose to use, bring a stove repair kit with an extra lighter and remember to keep your fuel away from your food bags to prevent contamination.
Small, sealable containers such as the ones Nalgene makes work well to fill with dill, oregano, basil, salt, pepper, cumin and paprika or whatever your favorite spices are. Your taste buds will thank you.