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.
Always have an easy to set up canopy available in case it rains or it gets too hot.
Don't forget to bring trash bags and Purell hand sanitizer.
Bring toilet paper.
Use frozen bottled water and ice instead of all ice in your cooler. It'll act as ice yet you can also drink it!
Have everyone bring their own beer and meat if you don't know their tastes. Make sure they bring extra for others.
Try to get to the same spot every tailgate so people know where you are. Also a canopy helps others find you.
Delegate duties to other people tailgating with you.