Polonius meets his fate by being in the "wrong place at the wrong time," but he is in that place because of his plan to spy on Hamlet as he and Gertrude have a conversation in her private rooms. This conversation is a "set-up" by Polonius, Claudius, and Gertrude. They hope that Hamlet may reveal what is making him act in a manner so not like his former self.
Throughout the play, Polonius is determined to be in the know about the Hamlet situation. He claims to have the answer to Hamlet's madness when he says that Hamlet is mad because of Ophelia's rejection of him. He is determined to maintain that theory as the play progresses, which is a sign of his desire to maintain his reputation for being right. At one point he even claims, "has there ever been a time when I have said, 'tis so' when it proved otherwise?" He wants to prove his theory so in Act 3 he sets up a conversation between Ophelia and Hamlet where Claudius and Polonius will then spy on them from a secret hiding place. This scene with Gertrude at the end of Act 3 is the the spy-session that does him in. Hamlet, thinking that the noise from behind the arras is Claudius, stabs through the curtain hoping to kill Claudius. When he kills Polonius instead he expresses very little remorse, calling Polonius a "wretched, rash, intruding fool." That seems to nicely sum up Polonius's character in this play.