I keep all of them but there are a few sets from cows and spikes I didn't take out. Some are in a bowl on my bench, some in a roll-away drawer, some in my archery tackle box, and I once found a set deep in the glove box of my old Mazda when I was cleaning it before selling
Big P - it's best to cut around the tooth with a caping knife then I wrap the tooth in a piece of cloth or leather and wiggle it out with pliers. You have to be careful because the jaws of pliers can crack the tooth or chip the enamel pretty good. I use boiling water to quickly to "flash" cook the tissue, then peel it off. Boiling the teeth for any length of time can actually crack them in half.