My favourite games are the ones where I feel connected to the people I meet, so yeah, pretty much any BioWare/Persona game ever made. I too easily feel emotion for these characters, upset when they're hurt, happy when they're joyous or full of humour.

BioWare really excels in this department though, I agree with you, Pike. Dragon Age in particular places considerable emphasis on your friends, which is happily continued with Dragon Age II and Inquisition (II has a rivalry mechanic, actually).