It is true that we do not get a sense of Polonius's interior self the way we do with Hamlet, so he is not a fully rounded character; but he fulfills important functions in the play. Most importantly, he is a plot device. When Hamlet accidentally kills him in a frenzy, mistaking him for Claudius hiding behind the arras, this action sets the entire second part of the play into motion.
In a parallel plot, Laertes now comes rushing home to avenge his own father's death, just as Hamlet is supposed to be avenging his father's death. Polonius' death allows Shakespeare to make Laertes a foil to Hamlet—if Hamlet is too hesitant in avenging his father, Laertes is too hot-blooded and, therefore, too easily manipulated by Claudius.
While alive, Polonius also has an important function. The consummate courtier and loyalist to Claudius, Polonius is two-faced, spies on Hamlet, flatters him, attempts to manipulate him, and in many ways proves that Hamlet is hardly crazy to believe the royal court is not a safe and trustworthy place for him to live.
Polonius provides comic relief as well: for all his efforts to help Claudius and Gertrude get to the bottom of what is troubling Hamlet, he has no idea, and the more knowledgeable audience (which knows about the ghost) can laugh at his fumbling attempts to, for example, show that Hamlet is lovesick.