The Two Towers
Frodo and Gollum
Frodo and Gollum are interesting to compare and contrast. They are both Ring-bearers, so they seem to understand each other in ways that Sam cannot. But Frodo is all about generous forgiveness and mercy and Gollum is petty, quick to take offense, and untrustworthy to the max. Even though the Ring has affected both of them, it has had a much harder time influencing Frodo than Gollum.
After all, Frodo inherited the Ring from his uncle and is willingly undergoing terrible hardships to destroy it, out of love for Middle-earth and his friends. Gollum's little friend Déagol found the Ring many, many years before, and Gollum murdered Déagol to get it. No wonder Gollum's soul has twisted into evil, while Frodo remains able to resist the Ring (at least, for now).
Théoden and Aragorn
Théoden is an older gentleman and a king to his own people. You might assume that he would be a model to Aragorn for how to be a king, since Aragorn has yet to take his own throne. But in practice, not so much: Théoden has the loyalty of his people, but he has also put them through tough times by falling prey to Wormtongue's lying advice. And even once Théoden is freed of Wormtongue's influence, he still falls into doubt and confusion during the battle of Helm's Deep, when things don't seem to be going well for his own side.
It is Aragorn who must reassure Théoden of the value of Gandalf's advice. Aragorn never loses faith in Gandalf, and he helps to lead Théoden's men in resisting the forces of Isengard. So Aragorn's relationship with Théoden actually proves Aragorn's own readiness to be king (which is lucky, since the next book is called The Return of the King).
Faramir and Boromir
While we only see flashes of Faramir and Boromir in The Two Towers, we do get a strong sense of how these two brothers compare with each other. In The Fellowship of the Ring, Boromir is tempted by the Ring and tries to steal it from Frodo. He makes up for this mistake by giving his life nobly in the protection of Merry and Pippin. But the fact remains that his pride and arrogance influences Boromir into acting wrongly.
By contrast, Faramir is less apparently warrior-like than Boromir. He's more of a thinker, and that's what helps him figure out what it is that Frodo is carrying. He knows that Boromir was tempted by the Ring, to Boromir's own shame. But Faramir swears that, unlike his brother, he has no designs on the Ring. Instead, he does his best to give Frodo advice and assistance before Frodo heads off into Mordor with Gollum. Faramir is less concerned for his own glory than for the safety and health of his city, Minas Tirith. His less selfish, more thoughtful nature means that he genuinely wants what's best for Gondor, a trait that bodes well for his future relationship with his king-to-be, Aragorn.