[Knight of Gondor]

Great discussion here. I would argue that Gandalf did not go only to save Faramir, but also to save Denethor, if he could.

I think all the points brought up are exactly why Gandalf (typically very decisive; he had to be!) had to pause and agonize over the decision. After a fateful confrontation with the Witchking himself, to let doubt assail him so heavily was very important. I think in the end, there were several reasons. Three have already been mentioned.

Personal: Gandalf was a mentor to Faramir, and would seek to save so noble a descendent of Numenor.

Political: Without a true Steward to surrender the throne to Aragorn, it might perhaps be a less peaceful transition of power.

Moral: Already discussed by others above. If I knew that I could choose to prevent either the president's assassination or the death of an innocent bystander, which would I choose? (I'm asking from an American standpoint, but just plug in your country's leader.) Most likely, the president's life would be the better to save in the long run.

The other two reasons I don't see discussed for why Gandalf chose the saving of Faramir are Foresight, and Leadership. As a Wizard, Gandalf was gifted with foresight. While he may not always have understood it, Gandalf's foresight was what sent Frodo and Sam -- the most unlikely of heroes! -- on the journey. It was the foresight of Gandalf that chose to bring Merry and Pippin on the journey -- a decision which, he pointed out, proved crucial in the long run.

Also, already somewhat covered under the political category, these warriors of old lived or died by their leaders. It was often very fortunate to slay the leader of a military group, because the it would scatter the troops and leave them leaderless. (Aragorn employed this strategy to gain exit from Moria.) Without a leader, it was quite possible that Gondor would not have the strength and devotion to fight. It was difficult for Gandalf to dissolve this devotion even to halt the guards from obeying Denethor's command.

In a lightning round of cost-benefit, Gandalf chose saving the leaders of Gondor over staving off the Nazgul.