Depending on the season, you may need a completely different set of tools. Here are some suggestions - cater this to your needs, what's in season, and how far from civilization you plan to be.
Clippers, small trowel
Clippers are great if you encounter a plant that isn't easily snapped off with your fingers. A trowel is often useful when digging up roots and rhizomes, but you can also generally use a knife.
Pocket knife or Steak Knife
Overall, a good thing to have. Use it for almost everything.
Plastic baggies, paper bags, baskets, wax bags
Different foods have different storage needs. You want to keep mushrooms in baskets or wax bags so they don't turn to mush, but maybe save some of those berry containers from the grocery store for collecting berries or other delicate squishy items.
Blackberry picking is like slow torture if you don't have the right equipment. I recommend having a pair of gardening gloves for those prickly and tough plants.
Latex gloves, Fels Naptha soap
In case of possible or actual contact with poisonous items. Try to avoid it if possible by wearing gloves, but if you forget, have the soap on hand to do a quick rinse-down.
Binoculars, Magnifying glass
Fine point permanent marker
I saw this suggestion online and love it. You can write on leaves or anything else you find, and immediately make notes about the item regardless of weather.
flashlight or headlamp
The woods get DARK, long before sunset.
Water bottle and rags or brushes
For cleaning anything while you're out in the wilderness.
Compass, whistle, maps
These are really for those trips where you might be far from civilization and maybe even far from a trail. Be smart.