I care about what happens to Alfonso Derecho Izquierda Quijano, the Kobold Paladin who's in love with a dragon. I want him to have an arc, I want him to grow as a person, and eventually I want his story to end - either in death on the battlefield, or having achieved his dream of wedding a dragon, or coming to the realization that he wasn't chosen by a dragon but that it simply coughed up some armor from a guy it had eaten while flying overhead.
Having said that, I also want to play some games where characters are disposable, including Paranoia. That's fun too!