What is the purpose of Fortinbras in Hamlet?

I always viewed Fortinbras as a foil to Hamlet. Over the course of the whole play, Hamlet whines about what he should do to avenge his father's murder. His only real actions are in a duel that was set up to trick him. On the other hand, Fortinbras spends his time in the background of the play approaching Denmark to claim what he views as the rights his family that were lost to older Hamlet. In the end, he is the one to take the crown because he has taken action.

I feel like I should mention that I once saw a particularly bad staging of Hamlet (by an otherwise very good director) where, at the end, Fortinbras comes in at the end of Hamlet with stormtroopers and machineguns everyone on stage, including the dead bodies.

I always saw him as a remote yet similar character against which to compare/contrast Hamlet. This seems intended in that both have fathers with the same name, and both are avenging the father's death. We hear small references to Fortinbras' progress throughout, and that in the end he reaches his goal seems to point to the fact that his gradual, steady effort was better than Hamlet's bouts of impotence or sporadic rash action. (I also have a theory that this appearance of a another prince as comparison, with Hamlet's apparent unfitness as a member of a royal family, points to the fact that Prince Hamlet is not actually King Hamlet's son; he is the son of the gravedigger [first clown], with whom he shares a talent and love for wordplay, and who started his job as gravedigger the day Hamlet was born, I'm guessing to get him away from the big house before the resemblance was noticed.)

As I read it, Fortinbras is impending responsibility. He is something/someone that the King of Denmark will have to face sooner or later, regardless of who holds the crown. Because for all the talk of kings and kingdoms, nobody does anything particularly kingly. Nobody rules. If the state of Denmark were an automobile, it would be off the road and in a ditch by the third act because nobody is at the wheel. Claudius has been enjoying the fruits of the late Elder Hamlet's estate, wife and kingdom and all. There are no counselors* wringing their hands at court, anxious that the King take up any issues of the day (contrast that with the opening scenes of Henry V, for instance). And dear Hamlet is too distracted by either his own grief or the inherited rage of his ghostly Father to give a moment's thought to what he would do should he ever manage to attain the crown. * - Polonius, you say? That poor doomed man is concerned only with assessing Hamlet's madness and sending Laertes off.

Fortinbras' approach is a ticking bomb adding tension from the beginning of the story. Without the threat of Fortinbras, so what if Denmark is off the road in a ditch, as grabbingsand has it? Fortinbras gives an immediacy to Denmark's need to get its house in order.

Well, for starters he's a parallel/contrast to the character of Hamlet (along with Laertes), sets H off on a famous soliloquy (4.4: "How all occasions do inform against me..."), and he's a source of closure for the State-level politics of the play (with or without stormtroopers).

I had a friend who suggested that Fortinbras staged the ghost of Hamlet's father (via some old school special effects) so that he could bring down the monarchy and take over at the end. A preposterous, entertaining, and clever idea.

Fortinbras secretly uses his quest for Polish territory (“a little patch of ground/That hath in it no profit but the name”) to gain passage to Denmark to take back the land that he believes is rightfully his. Like Hamlet, Fortinbras is haunted by the death of his father, but I think it's telling that Shakespeare never shows Hamlet and Fortinbras together, he is indeed a foil furthering the revenge theme.

I think of Fortinbras as an example for Hamlet of what he's supposed to be like - a Prince of Action, so to speak. Like Macduff and troybob said.