While I would agree with the "my mind" answer, my mind tells me that's not really what the question asked is referring to.
It's a tough call. I have managed to acquire some nice things over the years, but there's nothing I couldn't live with out. I guess the things I would consider "most cherished" are things that can't be replaced. Gifts and such from friends and family that have more than material value. Sure I could go buy another Auburn Tigers cap, but it wouldn't be my father's Auburn Tigers cap.