A Man's Man
Boromir gets a bad rap. Sure: he tries to steal the Ring from Frodo. But the spirit of Sauron can be totally overpowering—look at what it does to Frodo, Bilbo, and Isildur. Even the Elf Queen Bee Galadriel has to fight hard against it.
The problem with Boromir is that he's just a… man. In the film's introduction, Galadriel describes men as blinded to Sauron's deceit by their lust for power. And Elrond mocks Gandalf for putting his hope in men. Men aren't thought of so highly—and for good reason, considering the fate of Isildur and the Nazgûl.
So Boromir's problem is that he's a man, and his character is meant to be representative of the race of men. He wants to use the Ring for good and, while he's certainly not lacking in courage, refuses to listen to the warnings of Aragorn and others.
In fact Boromir acts as Aragorn's foil, showing that Aragorn's choice of exile over power as the King of Gondor and his refusal of the Ring when Frodo offers it to him are characteristics fit for a hero and a leader. Aragorn is set apart from normal men, but poor old Boromir falls into the traps of darkness:
BOROMIR: What chance do you think you have? They will find you. They will take the Ring and you will beg for death before the end. You fool! It is not yours save by unhappy chance... it might have been mine. It should be mine. Give it to me! Give me the ring.
But let us not forget Boromir's more lovable moments. Not only does he have a grand old time teaching the hobbits some sword fighting skills, he also has a touching scene with Aragorn in Lothlórien: he tells Aragorn that he would follow him to the end. This is a big change from his "Gondor has no King" attitude when they meet in Rivendell.
And after the Ring has finished consuming Boromir he appears immediately regretful and puts his life on the line to save the hobbits. He dies muttering his apologies, and Aragorn assures him he will not have died in vain.