Put dry ice at the bottom of your cooler to prevent the rest of your ice from melting.
Use an old tool box to store your utensils.
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.
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.
Bring a bit of styrofoam padding for your feet during cold weather events.
Try to do most of the prep work before leaving. Examples include making the burgers and marinating the meat.
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.
Delegate duties to other people tailgating with you.
If you're bringing bottled beer don't forget the opener.