Put dry ice at the bottom of your cooler to prevent the rest of your ice from melting.
Buy a tin foil pan if you need to bring a lot of food or meat. When you're done it can be simply thrown out instead of cleaned.
Do something to uniquely identify your drink so others don't drink it: partially crush your beer can, have an odd color cup, use a marker, etc.
Use an old tool box to store your utensils.
Wear the team colors and if you have it bring the team flag to put on your car or a pole.
Bring mostly finger foods to keep things easy.
If you're new to tailgating walk around the tailgate area before the game and take notes on the good tailgate parties.
If you don't have tickets to the event and can watch it on TV, go tailgating anyways and bring a generator and TV!
Hot cider, hot chocolate, a little Baileys Irish Cream all go a long way in keeping you warm in the cold.
Always have an easy to set up canopy available in case it rains or it gets too hot.