Washing broccoli is always good idea. It gets rid of grit in the vegetable, but you probably want to know if it also gets rid of bugs. Any produce you buy could have insects on it, but with broccoli they could be hidden deep in the crown, unaffected by a simple rinse. Though bugs aren't a common problem with commercially grown broccoli, a good soaking won't hurt and could help get rid of any insects lurking in your florets.
The Soaking Process
Remove the leaves and woody parts of the stalk and cut the broccoli into bite-sized pieces before soaking it. Immerse the cut pieces into a salt water solution for 30 minutes. Use 4 teaspoons of salt for each 1 gallon of water. Any bugs in the broccoli will float to the top. After soaking, drain and prepare the broccoli as you normally would.