A WAY TO REPURPOSE USED GAMES WITHOUT LOOKING LIKE A TOTAL CHEAPSKATE
The thing about board games and other games in boxes is that you really can't get away with giving them as gifts if they've been used at all. The scuffed-up or falling-apart box makes it look decidedly sad regardless of how good condition of the game pieces actually are (not to mention the tape marks from the secondhand store's attempt to keep all the components together).
If you find yourself in such a situation, just craft a new box, bag or other container for the game. A simple wooden box could turn an old mass-produced game into a beautiful heirloom. A bag made from vintage t-shirts could amplify the nostalgia of a favorite childhood game.
I don't have any photos to share because I've never actually tried this, but doesn't it sound like a good idea?