I like to use elastics for the spools of thread because I found that tape left a sticky residue, and I hadn't thought of some of the members of this board's resourceful suggestions.
For bobbins, no matter how well I wound the thread around, my bobbin case always had a mess of threads all over everytime I opened it. I tried the mini pony tail holders, which held the threads tight on the bobbins; however, they obscured the colour of the thread that was on it.
Then I read a tip that works really well. Go to your local hardware/home supply place/aquarium shop and get some clear tubing. Use a sharpie or a similar pen and make a little mark on the tube that is a bit smaller than the inside width of your bobbin. Then, on the opposite side that you made your marks, cut straight down the clear tube so that it can open up. Once you do that, you can just cut across the tube where the marks are. You end up with a bunch of rings with a slit on one side that you can open up like the letter "C" and slip over your bobbin. Hope that makes sense-- it would be a lot easier if I could just draw a picture. Most of us quilters are pretty visual people!