Aragorn, Frodo and Sam still to come.

Gandalf
Gandalf at times seems something of a father figure to Faramir. Michael Martinez' words are useful here: "When Gandalf came and tolerated Faramir's natural inquisitiveness the prince found a valuable mentor which his father had refused to be." It's interesting to imagine what kind of relationship they had when he was a younger boy. The appendices note "he welcomed Gandalf at such times as he came to the City, and he learned what he could from his wisdom." Evidently they did have some exchanges - for example, Faramir tells Frodo in Ithilien how Gandalf told him of his many names and that "I first saw him when I was a child, and he has been twice or thrice since then... and I learned a little of him, when he would teach." Gandalf in turn shows that he has some affection towards Faramir (in as much as Gandalf CAN show affection): he defends Faramir when Denethor voices his wishes that he should have gone to Imladris in the stead of Boromir. When Faramir returns from Ithilien under the shadow of the Nazgul, Gandalf rides out to aid him. He tells Faramir not to throw his life away in bitterness after his father sends him harshly into battle. Finally, he saves Faramir from being burned on the funeral pyre and tends to him in the Houses of Healing. The relationship between these two was atleast strong enough to invoke jealousy in Denethor... and is a big part of the tension between the father and son.

→ (to Denethor) "He would have gone [to Imladris]. Be not unjust in your grief."
→ "I must come, since no other help can reach him."
→ 'Faramir and Éowyn and Meriadoc were laid in beds in the Houses of Healing... Gandalf went from one to the other full of care.'

Beregond
"A man of arms of the Third Company of the Citadel." Pippin describes him as "tall and proud and noble." His son, Bergil, helps cure Faramir of his illness by doing an errand for Aragorn - collecting Athelas. Beregond is a fascinating example of the love that Faramir's people bore for him. When Pippin asks him to "choose between orders and the life of Faramir," Beregond, quite simply, chooses the life of Faramir. He commits treason by leaving his post without permission, killing the warden and two of Denethor's servants that try to bring the torches to the House of Stewards that will kill Faramir. He defies Denethor, the Lord of the City himself, for Faramir's sake, placing himself in front of his Captain when Denethor comes at him with a knife. However, Beregond is pardoned by King Elessar, and moreover made Captain of Faramir's White Guard. He is certainly worthy of the job, obviously a skilled swordsman. And apparently Emyn Arnen will suit him - he tells Pippin "I love beasts, and we see them seldom in this stone city; for my people came from the mountain-vales, and before that from Ithilien."

Pippin
Pippin admires Faramir almost without limit, as we can see by his first impression of the man (read the entire quote here). Pippin becomes a great asset to Faramir... without his help, it is likely that Faramir would have been burned on the funeral pyre. When Pippin realised that Denethor was going to take him to the Silent Street to burn, with Faramir's death still in question, he seeks out Beregond and Gandalf to help save him. And in a touching dedication, Pippin names his first and only child after Faramir.

→ 'When he saw the pale face of Faramir he caught his breath... suddenly for Faramir his heart was strangely moved with a feeling that he had not known before... He knew now why Beregond spoke his name with love. He was a captain that... he would follow, even under the shadow of the black wings.'
→ "Poor Faramir! Quite likely he needs medicine more than tears."
→ 'Pippin poured out his tale, reaching up and touching Gandalf's knee with trembling hands. "Can't you save Faramir?"'