Bobbins and spools together
 

The beads & jewelry making supply department has little plastic bags. Usually 100 bags in a package. Just the right size for storing a bobbin & matching spool of thread.

I have a board in a drawer that has small dowels inserted in to it - I place the spool on each dowel, with the bobbin sitting on top. (I also have that clear stretchy wrap I put around the spool to keep the thread from unwrapping, and I have bobbin keepers to keep the bobbin thread contained.)
I actually have two desk drawers set up like this. Best idea ever for me!

I love the little bags and have 2 different sizes. I wind 4 bobbins and put in the bag. Mark the bag with type of thread and they are ready to go.

Another bag holds an extra machine foot. I put an address label on it. It's stored in the machine compartment. Ready for class.
Special buttons for clothes are stored in a bag and labeled. Easy to find in the button box later.

I found the plastic bags too slippery to contain them altogether.. How do you store the filled bags?

I have a container and put the bags with sorted buttons in it.