I keep all my good Pokémon on a game that I can backup the save file for, as well as on Pokécheck.. So I would keep the most valuable stuff (the Pokémon) but lost the other progress, as well as access to certain things. Meh.
I started backing up my game files and buying multiple copies of games for games I REALLY love, after I lost my first Pokemon Blue file to dropping it while in the Super Gameboy gamepak, so while it would be less of an issue for me I'd still be pretty pissed.
*looks at Mega Memory Cards for GBC games, GBA SP USB Backup Adaptors, Pokemon Box and DS Backup Adaptor*
Currently playing: Animal Crossing DS, Pokemon Platinum/Heartgold(JPN)