Maybe it's an odd thing to be attached to, but I have a Sega Master System (and the games, accessories, etc.) in my basement that I just can't bear to get rid of.

Aside from being the first game console that I ever owned, I used to play SMS games with my Mom. Dad and I are both pretty geeky, but Mom isn't - and yet she'd still play SMS games with me every day. I remember always having a problem getting past one part in Wonder Boy, so every day before I got home from school, she'd start playing the game, get past that point, and then we'd pick up after that point, taking turns from there.

I kept playing games as I got older (surprise!) but I could never get her to try the more 'complex' games that I got into later in life - still, I cherish those memories.

tl;dr Can't get rid of old game console because I love my mom.