I've shot a video that shows exactly how I trim my competition briskets. If I was cooking this brisket at home for friends and family, I wouldn't trim nearly as much as I do for competition bbq.... but my goal is to expose as much of the meat as possible.
You want to ensure that your dry rub and your smoke can penetrate the meat and build a perfect bark. If you don't trim your brisket properly, then you will have large fat deposits that never render - just sit on the top of the meat, block the flavor and hurt your meat's true potential. 
This is the competition-style way... which is a little more in-depth that your average backyard BBQer will follow, but this method will give your meat maximum smoke penetration, it will prepare your brisket for making your "burnt ends" and simply give you the best quality product.
How to Cook a Brisket | How to Trim A Brisket | Tips On Cooking Beef Brisket | Brisket Injection | Brisket "Burnt Ends"