You should be scrubbing your grill after every use with a wire brush. If you use your grill weekly, you should pull your grates and thoroughly clean them once a week.
It's not just about the general importance of keeping things tidy — a clean grill significantly affects the food it produces and makes the grilling process much safer.
You should also dive into the guts of the grill and clean it from top to bottom at least twice in the summer. This will make it last longer and maintain a shinier, cleaner look.
A mixture of water and kitchen soap applied to a wire brush will take care of most of the caked-on mess, but for the stubborn stuff, vinegar and baking soda work best.