I keep most of mine in a Fish & Tackle box my thoughtful husband gave to me the Christmas after we were married. It's not pretty but it's pretty handy!
I also found a cute thread rack at a craft fair years ago, and just googled "wire sewing machine thread rack" to find a dozen sources that you can buy these ranging in price from $17.95 to $29.95, holding 23 to 67 spools of thread.
I keep my bobbins (and buttons and wooden spools) in a clear old-fashioned canning jar on the window sill.