I'd say throwing away the boxes of my Game Boy, Game Boy Color, and N64 games is by far the ultimate damage I've ever done to anything in my collection, and I'm sure it's the same for most other collectors. Other than that, all I can remember is toppling over a small tower of PS1 games once while carrying them to another room for cleanup.
And I'd advise anyone against using magic erasers, they do more harm than good.
Just the other day, damaged a Wii U disc thinking I could clean marker off of it with isopropyl alcohol. Don't do that.
My solution? Re-buy the game, BRAND NEW, like I should have in the first place. Used games just piss me off. Not worth saving a few dollars to get some jacked up copy for less, in terms of modern games. In fact, I'd recommend passing on anything that's written on unless you're happy with that kind of jank. If you try to fix it, you'll just make it worse. Gotta have standards for what's collectible versus what's not. Trashed up copies are not worth collecting IMO.
I have before with stickers or accidentally torn maps and manuals. I now use Bestine to remove any dirt, stickers, glue, disc labels, etc. Stamp collectors use it to remove stamps from things. You just use a q-tip and let it soak for a minute or two and the sticker comes right off and the ink or whatever underneath isn't touched. I've been using it for years now. If it's a metal label or stickers you just pry up a small corner and start swiping underneath and slowly pull up. The only downside is that it evaporates quickly.
You can achieve the same results with acetone with the added bonus it will also dissolve the adhesive—or make it easier to remove if any residue should remain—whereas heptane just removes the sticker while leaving the sticky residue behind, at least in my experience. Not to mention, acetone is less harmful.