I don't know if mine counts at all since it's not materialistic, but I mostly get attached to the plots. I prefer to play my games along with the storymode, and if played right it's like an epic movie,, of which you're involved in. If the plot sucks but the gameplay is good, I just can't play nor buy the game.
But if it were materialistic, it'd have to be the bow in AC3. I know they're going to remove it in future games, but the thought of it leaving kills me. It's just too epic IMO. Much better than the crossbow and musket.
My soldiers and pets. Anything that I have to name, basically. Character class-based fighters, Chao, Pokemon, my Phantasy Star characters-- those types.
Otherwise, I grow quite attached to my Fire Emblem characters and Final Fantasy Characters.
I know I always get attached to my first set of tools in minecraft and my sentries in tf2.
how about you?
(you can share characters too if you want)