I use this. It cleans everything off down to the metal. What doesn't burn off simply flakes off with a light brushing. Takes about 15 mins from grime covered grate down to clean metal. The sound it makes when it's on can be a little intimidating.
I use this method: Get a large wash tub. Fill it half full with almost boiling hot water. Add 1/2 to 1 cup of ammonia. Put the gates, FlameZone covers, triangular grease shield and cooking grates into the tub. Let soak for 30 minutes. In the meantime, clean the inside and outside of your grill.
After soaking, use a scrub brush or #3 steel wool to clean all the parts in the wash tub. Rinse under hot water. Dry and place back into the grill. Works like a charm and the ammonia is cheap! Get a gallon of it at Lowes for $1.69.
Cranking the grill up to HIGH will help burn the gunk off, but the grills are regulated to not go above 500, so most people use other methods to better scorch the stuff off.
If you have a self-cleaning oven, those work pretty well to burn off the gunk, if you don't want to go full "RAMBO" mode like Scott!!
The grease from the grates can gunk up the dishwasher, so you'd be better off scrubbing in the sink instead. Like BBQJUDGE said, they're stainless, so you're not going to damage them by scrubbing too hard. Pre-soaking them in boiling water and a cup of ammonia will loosen most of the grime and make the job easier.