My mother once owned an embroidery business, and the way she dealt with her thread was to pre-cut it to length, then twist or braid it back into skeins. With the cut-to-length skeins, you can remove a single strand of thread while leaving the rest of the skein intact.
(Note that this method works best for perle cotton, i.e. the type of embroidery thread that's already twisted into, well, threads, instead of individual strands of floss. If you use it for stranded floss, you need to be careful to remove an entire six-strand thread at once, and only separate out the number of strands you want after you've removed it from the skein.)
A skein winder can be very useful for this purpose, but in a pinch, an appropriately-sized piece of cardboard can work just as well. You remove the paper from a skein, find the end, and re-wind the thread, either around the skein winder or around your cardboard.
When it's all wound, you tie a small piece of string around the threads at one of the arms (or one edge of the cardboard), and then you cut the skein in half opposite the tie. Now you can either twist the two halves together -- twist each part clockwise, then twist the parts together counter-clockwise -- or you can re-divide the skein into three parts and braid them together. Don't twist or braid too tightly.
Firmly tie off the ends of the braid/twist with an elastic, so it'll continue to hold together as the skein gets smaller. When you need a thread, grab it at the fold and pull it out. The skein will get all accordion-pleated and scary-looking as you're doing this, but it'll smooth right back out after you have your thread.