I'm pretty LNT, but I'll bring something home depending on how cool it is.
If it's pretty cool, like a nice piece of quartz, then I'll pocket it and bring it home. If it's something really cool, then I usually leave it behind for other visitors to enjoy...e.g. a huge crystal or quartz or an old lantern with ferns growing out of it.
But then, if it's really REALLY fucking cool, I'll take it, e.g. the piece of petrified wood with crystals encysted in the rings, or an old coin. Finally, if something is a priceless artifact, I'll take it and give it to a museum (though I've never found anything like this).
Most organic natural artifacts (skulls, feathers, etc.) I take, since they get replenished. When I collect enough, I make a "bone shrine" somewhere in the middle of the woods. Basically a sculptural arrangement of bones meant to freak out some hikers.