Poster #2s & 4 gave you a pretty comprehensive list but I'm going to add to it:
If camping in bear territory double check with the campground to make sure you don't have to have a bear safe container for your food. (Bears can, will and have torn the doors off of cars to get at food.

)
A pocket knife to cut the rope. If it rains sometimes it won't come unknotted when it's still wet. Most campgrounds don't mind you putting it up but they get mad if you leave it behind.
Test your rope before you leave to make sure it will hold a knot and to make sure it won't stretch a ton when wet.
A hammer with nail puller ends or mallet with a pulling loop on handle. Many a time we have had to pound down hard to get those pesky tent pegs into the ground or need a little extra pulling power to get them out.
A canopy is easiest for set up but if you don't want to spend the money on it a tarp strung over the picnic table is also a good option if there are trees available.
A ROLL OF QUARTERS!!! While the numbers are dwindling many a campground in an area of low or expensive water supply will have a pay shower. Usually you get about 5 minutes for one quarter. But sometimes it's less time for more money. Also, if it rains you a quick trick to make you more comfortable at night for sleeping is to take your bedding and throw it in the dryer for about 10-15 minutes to drive the dampness out. Throw PJs in too. It's just more comfy.
If it's going to be cold at night make sure to bring an extra blanket to put between the sleeping bag and the air mattress. We discovered to our regret that the temperature of the air in the air matress is the same as the temperature outside (okay this was a duh moment but hey we were young). Well this means that you could be sleeping on top of 40 degree air

It can make for a very cold and restless night. An extra thick blanket put under the sleeping bag provides insulation and absorbs any condensation from the air inside the air mattress.
Everyone wants to blow up their air mattress at the same time. Be prepared to wait if your pump is electric. We went somewhere recently where they had banned them in the bathrooms so be prepared to blow it up using
your air. Also, don't blow it up so much that it won't fit through the door of the tent but make sure it is firm enough that when you lay on it you don't sink to the ground.
At least one large jug for water. A couple empty gallon milk or juice bottles work well. No need to spend money on a container. Sometimes you have to walk a long way to get it.
Unless you are camping at the beach take your shower at night right before you go to bed - there is actually more hot water and it's easier to get in to the shower. At the beach take your shower mid afternoon - right before supper.
Plan to have your kids get really really dirty. It's okay you're camping. We usually take them into the shower with us but sometimes we'll let them go all weekend without bathing.
Let the kids have at least $1 to get something at the camp store (see the above quarters). It's a vacation for them and they will want some sort of souvenir. Usually a popsicle will do it.
Bring bikes at the very least for your 5 yo. Sometimes it's a long long walk to the camp store. Also, my kids love to just ride around the campsites.
One final tip make sure that you don't leave anything resting against the side of the tent when you sleep or if you leave for the day. If it rains water will seep in right where your stuff rests against the side of the tent.
ETA - even if you plan on drinking bottled water you will still want the jugs for water because unless they have a dishwashing station you will need it for washing your dishes.