Folks, this is getting to the heart of one of my unfavorite parts of the movie trilogy: Peter Jackson totally failed to get the basic meaning behind the character of Faramir (and, to a lesser extent, Aragorn).
Look, we all know that for two ages of the world, the dominant culture was the elves. Now, the elves were pretty decent people, and they did a good job of caring for the land, but they weren’t exactly perfect. The First Age ends up being full of strife over some trinkets that Feanor puts together in his spare time. The Second Age ends up being filled with strife over some trinkets that the elves near Moria put together under the influence of Sauron, which, you have to believe, came about to some extent because elves just can’t help but think that running things with the help of little shining trinkets is a Good Idea.
Now, it’s the Third Age, and mankind is coming into its own. The age will end with the passing of the Elves, these wise, kind folk who have tried for the most part to make the world a better place in which to live. Humans, we know, are greedy, grubbing folk who will sell their mother-in-law for whatever the market rate is. We can’t expect much from humans, can we? I mean, look at our world now, and compare it to the world of the Third Age! Yikes!
But that’s the whole point to Faramir and Aragorn. Here are humans, both of which are in need of power. Each has the chance to take the Ultimate Weapon and use it to gain the Ultimate Power. And each passes on it, each for their own unique reasons. Humans may be flawed, but we have the CAPACITY to be very good people.
Faramir, especially, is in the story to show that we shouldn’t fear for the world under human rule, because humans CAN be good. The contrast between Faramir and Boromir couldn’t be more plain, and wasn’t just put there out of happenstance.
And Peter Jackson totally ruins the whole thing by changing the story. Faramir becomes just like any other human: unable to resist the temptation of power and greed.
To answer the OP: Aragorn isn’t tempted because his value system is such that the “rewards” of the Ring aren’t interesting to him. He knows enough to know that the Ring is a deception: he cannot truly become what he wants by using it. And since he isn’t interested in power qua power, that means the temptation, if it exists, to take the Ring simply isn’t very strong.
And think about it: would YOU give up a chance to have Liv Tyler as your wife for the chance to have orcs as your slaves?? 