Grill - Matter of preference, but I use charcoal.
Fuel - You need to make sure you have enough charcoal - or gas. It would suck to be cooking pulled pork - which takes about six hours - only to run out of fuel in the third hour.
Chimney Starter - This is one of the greatest inventions for charcoal users. You put newspaper in the bottom, pour charcoal in the top, light the paper and you have ready characoals in about 15 minutes, without the lighter fluid flavor.
Grill Brush - Used for cleaning off the grill. You can get one under a buck at stores like Wal-Mart or Shopko.
Mitts - Get a couple of BBQ mitts. They cover your arms also, so you don't get that nice singed hair odor.
Spatula - This is one of two utensils that you will need. Use this to turn burgers. (You can buy an entire BBQ set, complete with spatula, tongs, fork, skewers and basting brush for less than ten bucks at your local Wal-Mart.)
Tongs - Use this to turn almost every other type of meat.
Basting Brush &/or Mop - I use a mop more than I use a brush. I think it spreads out the sauce a lot better. Get a few for different sauces.
Meat Thermometer - This is almost as important as a grill. You don't want to serve undercooked - or overcooked - meat.
Apron - You don't want to get grease and charcoal all over your "I'm With Stupid" T-Shirt.
Other Things That Are Not Necessary But Help the Whole Process
Syringe - Use this to inject flavor into the meat before grilling.
ChickCan Rack - For making the most tender chicken you could ever grill, using a can of your favorite beverage. (Recipes coming for this)