In Cave Story 3D I went into Curly's room in the Sandzone and picked up the item, "Curly's Panties". They are descriptionless and I could not find any use form them for the 3DS version. Do they have any use at all except for sitting in my inventory, taking up space?
It looks like in Cave Story+ on the PC and Wii, at least, finding them unlocks Curly Mode from the main menu. It's kind of unclear whether or not that mode is present in the 3DS version; I've seen comments on the internet going both ways.
In the PC version, they do have a description, which ends with:
They have no use.
Regardless of which version you're playing, they're not used during the game itself so they'll just sit there in your inventory taking up space.