The modern self-adhesive stamps are uncollectable as far as I’m concerned, which simplifies the hobby quite a bit. The older gum-type stamps are fun to soak off the envelope (if you collect canceled stamps as I did).
I've kept a few of the high denomination kind ($2 and more) from friends and family to whom I have sent packages. I've just asked them to cut off the whole square around them and include in the next letter of package heading my way.