Depending where you are going for the picnic if no picnic table you will need something to sit on and serve the food, blanket. Even if the food isn't messy you should bring something to clean up with: Napkins, wipes, etc. Extra sunscreen, something for insect bites. A group game, ipod attached to speakers with appropriate music. A trash bag.
I never think a picnic is complete without deviled eggs and baked beans :)
My friends and I had a nice picnic last week, we had thought about what to cook for the picnic and my idea was to make Chicken Arrabbiata, I myself didn`t know about the thing but my wife found the recipe somewhere and suggested our making the stuff, I should say the idea was really great, we enjoyed the thing really much, I think you could try preparing the stuff too, you won`t regret it, it`s guaranteed!
I live where it is hot and humid, so I prefer food that is cool or cold. Sandwiches, coleslaw or potato salad, and something cold to drink. Oh and here is a tip. If you make your sandwiches in advance, leave the mayo and mustard off until you are ready to eat them. It will keep them from getting soggy.