Question: What are some grilling tools that a beginner should have when purchasing a new grill? Additionally, are there tools that are useful for the more advanced outdoor cook?

Answer: 
Tool-wise: spatula, tongs, grill brush (for cleaning) and a basting brush. If you're using extremely hot fire or high flames there are grill-safe mitts you can buy.

This isn't a tool, but I find buying cedar (or other wood) planks for grilling fish and other meats and veggies on are invaluable. Similarly, applewood or hickory chips for smoking.

As you get more advanced, there are rotisserie attachments for most grills, but they can get pretty pricey.

I agree with justkt that metal skewers are extremely useful, as well as the grill basket for certain fish and veggies.
I have a wide, flat knife that can be used as a spatula; I find it really useful. Everything else has pretty much been mentioned, but I would suggest a pair of tongs with decent teeth on them. It's very disheartening when that burger or steak slips out of your grip and into the coals or onto the ground.