The cast of Uncharted 2 is one of the best out there, and I cared about everyone (well, except the "big bad", but eh). If you don't feel for Nate in the first two minutes, just shut the game off, it's lost on you. :P
Final Fantasy X always resonated strongly with me, and in FFXIII I absolutely love Snow, but my favorite character in the whole series is FFXII's Basch. "If I could spare but one person from war's horror, I would bear any shame. I would bear it proudly." Whereas most characters in the series are varying shades of selfish (which always makes for interesting character clashes), Basch struck me as being the most selfless. He was kind, strong, and willing to do what was right no matter the cost on himself.
I'm tired, so I'm going to let this degrade into a list of other games that had characters that strongly affected me:
--Okami
--Ico
--Shadow of the Colossus
--Vagrant Story
--Beyond Good & Evil
--Psychonauts
--The Legacy of Kain Series
--Suikoden II
--Shin Megami Tensei: Nocturne
--Digital Devil Saga (1 and 2)
--Metal Gear Solid 4: Guns of the Patriots