Having done my own auto work for years now, I’m starting to amass quite a collection of parts. I’m something of a minimalist, and don’t like to keep things I’m not going to use, but I know some of these things have some sort of value as cores (water pumps, alternators, a/c compressors, carbs, etc…) so I’d hate to just throw them out.
Would an AutoZone or O’Reillys take them as donations? Or is there any chance I could sell them to a Reman’er myself?
What do you guys do?
Ask them but I seriously doubt it.
A remanufacturer is unlikely to take them from you.
But attached to a rope they make great boat anchors.
Yes you need to ask first, but so many parts systems demand one-for-one core exchange that I doubt you’ll be able to get any money for any of it, let alone give it away.
I don’t get their logic and have argued up and down with my own Ford rebuilder for years.
" so where do they get another one to rebuild ? Take this one ( free ) and at least put it into the system."
“nope, can’t do that”
So a perfectly rebuildable engine goes to the trash.
No core brokers will ever come to this small town looking for inventory. 
I guess one reason they wouldn’t is they need to know exactly what part they have, and a one-for-one exchange insures that (mostly). Reminds me of some huge collection of cars and parts that went up for sale on Ebay several years ago. Acres of cars, shelves of parts, but nothing identified. What do you do with a box that has 20 unmarked distributors in it? Beats me!
Being truly green find people to rebuild the parts and save them for future need or sell them as rebuilt on ebay. Check the rebuild vs the new price before doing so. I am considering having the local guy rebuild a power window motor I had to replace just for stock. At worst option a metal recycler may give you a little cash.