This thread really made me think since most things could always be repurchased. It would reeeeeally suck and would cost a lot since game stuff costs way more nowadays, but it is possible. However, there is one thing that I haven't parted with no matter how tough things got, and that's my beat up old boxed copy of King of Fighters 95 on the gameboy from when I was a kid. I got it on release day and although Fatal Fury 1 was the first SNK game that I played in an arcade, King of Fighters 95 was the game that really stood out to me and hooked me on all things SNK/Neo. Although not a big deal today, the ability to bring kof with me was almost unreal and I spent a TON of hours playing the game, thumbing through the manual's art, and carrying the game's box to and from school.
I met two life long friends through chance inquiries while playing the game ("Hey whatcha playing?") and couldn't see myself parting with this copy even though it's long been made obsolete via other kof games on ngpc, gba, psp, vita, etc. Good times!