HA! Currently? Piled in a drawer (so embarrassing)
What I used to do was get those desk organizer things you see in offices, with the vertical slots for storing file folders upright. Instead of using them with manilla folders I would use them for my 12x12 papers. It was just a cheaper way for me than buying drawer sets that would fit them although I did see some at IKEA I drooled over for a while.
I'll throw another question out there - how do others store their scraps of paper? Waste not, want not echoes through my head when cleaning up after a project and I save all the bits that are of any decent size. I've got quite a stack of bits now! Especially since I started using the Cricut more heavily!
Mine are in a plastic tub. Was thinking about changing it to a different tub Then sorting them by color and theme Either put in zip lock bags or file folders.