Faramir's is a very peculiar character in LotR. He's the younger brother of Boromir (from The Fellowship of the Ring fame), and his father's Denethor II, the Steward of Gondor. He's the captain of the armies of Gondor, and when we first meet him in The Two Towers, he's hiding out behind the waterfalls of Henneth Annûn in Ithilien with a band of spies, trying to figure out what the forces of Mordor are up to.
So why is he so strange? Well, not to put too fine a point on it, but he's perfect.
There is nothing that Faramir does to make the reader question the fiber of his being. He's appropriately suspicious of Frodo and Sam, and initially we worry for the two hobbits' safety and mission. But Tolkien tosses those doubts out the window the minute Faramir makes his famous speech--I would not take this thing, even if it lay by the highway...
Like Aragorn, Faramir demonstrates the strength of blood of the old kings of Númenor. He is, in fact, part Silvan elf (from his mother's line), though he certainly seems to take after his father. He shares his father's perceptiveness of others, as well as his efficient and just demeanor. But, while Denethor II is decidedly paranoid of others' intentions, Faramir is more hopeful.
Faramir puts his perceptions to good use when he first meets Éowyn in the Houses of Healing. He openly proclaims her beauty, then openly declares his love for her, and THEN reflects her obsession with Aragorn so that she can understand it. In this way, he wins her heart.
Having such an infallible, honest, perceptive, courageous, calm, AND just character in LotR is both refreshing and annoying. On one hand, we are given a human character we don't have to worry about--when all humans seem to be subject to the slavery of the One Ring (even Aragorn). Faramir is a well-placed pillar under a shaky roof. His problems are external rather than internal, and his emotional strength is unmatched.
On the other hand, Faramir's incorruptability is almost too perfect. There are times when his behavior is predictable.
Perhaps most interesting about Faramir is his relationship with his father, who openly admits that he prefers Boromir over him. Despite this, Faramir maintains amazing cool, and is able to put the good of Minas Tirith ahead of his own conflicts with his ever-maddening father.
One of Faramir's only "fights" comes in an argument with his father. While other characters engage in physical combat to prove themselves, Faramir engages in another type of combat entirely. That this is his only true "battle" in the story creates for the reader a sense of rarity in Faramir. He is never on the offensive, always a protector, and an amazing example of pacifism at work in LotR.