Well obviously it has to be a beat up disc as anything new is easily replaced with another new disc. Of course, I throw Discraft and rumor is this tendency is not universally true.
I actively build backups against the risk of loss including trading for beat up versions of the staples in my bag. Good thing too as a couple weeks ago a beat up 1st run Z Tracker cracked on me, not even on a throw ( I didn't know candy plastic could crack. Slice or gouge sure but crack?). The 2nd string has stepped forward very well or this now deceased disc would have been my choice as most missed.
Now my vote goes to my most beat up X Buzzz. This was a Christmas gift from Discraft with a Christmas custom hotstamp from maybe a decade ago, the stamp long worn off by use. This disc is an absolute upshot staple getting more use than the other 3 Buzzzes I carry combined. Last winter I faced a very risky drive (very risky for losing it) so I had a buddy (an experienced Pro player) go around the blind corner to spot it. He reported it went over the basket and was no more than 30 feet long. We looked for a long time. I returned twice on my own and put in at least an hour in further fruitless search.
6 months later I got a call it had been found, evidently 100 feet past the basket in an impenetrable swampy thicket. When I got it back it fought its way back into the starting lineup. As many of you know, within a few weeks of replacing a lost disc you learn and adapt to the replacement so well it is hard to kick it out. But from regularly playing a few courses with lots of water hazards, the formerly lost disc filled in as a Risk Disc and proved its value.