Lots of fab potential alternatives to the Mariah Carey-esque wrapping room I would really like on pinterest...but I've actually given up on that
and keep everyday birthday stuff in a drawer
with sellotape and scissors and stickers (so that there's no chance a tag can come off)
I do have a separate box for ribbon but I am VERY tight with my ribbon and only give it VERY special people 
Have xmas stuff in a box in the cellar (we don't have a loft)