I’m talking about stuff that is seriously ripped and torn.
I just know somewhere in the world somebody wants and can use this stuff. Where are they? How do I get this stuff to them?
You could cut them up and make them into rags. Good for handwashing your car, or dusting your furniture. Or, cut them um into strips and make a rug.
A friend of my moms takes her old torn up cloth to a guy that makes multi-color rugs out of them. He gives her a few in return and sells the rest at a flea market. They look good in a kitchen or bathroom in front of a sink.
I am not sure that this will pan out for you, but just in case:
So do a Google on “shoddy padding” and good luck. 
Surely there is someone out there who would want your clothes for making rag rugs or quilts. You could cut them up in uniform little squares and sell them as “quilting squares” on e-bay. People will buy anything if it’s on e-bay. Check with local churchs and retirement homes, or, call the Salvation Army. I am sure they get stuff that is too worn to use, how do they dispose of it?
Save the buttons! 
Well, if you don’t want to cut some up to patch the others and you have cold winters in a draughty house, you could make a door sausage (draught excluder) .
You could cut the better parts into squares/hexagons and make a patch-work quilt, or cut them up for patchwork using pinking shears (zigzag scissors) and give them to a local “womens institute/sewing guild” so that they can use them for patchwork.
I believe that people use cotton and other natural fibers for handmade paper? You could call up an art supply store or the art department at a local college.
Your old tighty-whities could be reincarnated as a Chinese landscape. Perhaps they’ll become the canvas for a Buddhist sutra. An allegorical story about karma, no doubt. 
In many cities and towns there are receptacles for old clothing to be used by charitable organizations. They’re usually green and about the size and shape of a dumpster. If you read the information about what to deposit, there’s a notice that says you can drop off rags as long as you mark the bag or box “Rags”. Also, in some communitities there are similar receptacles that only accept rags for recycling. If you have old towels or cloths, your local animal shelter would love to have them.
Well, Ginger of the North took all my Too-Trashed-For-The-Thrift-Store stuff last time I cleaned out my closet and was going to use it to make quilts. There is a chance, depending on where you’re located, that she might be interested in your stuff too. However, I think right about now she’s knee deep in wedding plans, so you may have to hold off for a month or two.
I read somewhere that if you take the ratty clothes to a thrift store, they will sell them to third-world countries or sell them as rags. So either way, they still make use of them.
I second the idea of a pet shelter. More specifically, a ferret shelter. As a foster parent for ferrets and ferret owner, believe me, they can use them!
“I read somewhere that if you take the ratty clothes to a thrift store,
they will sell them to third-world countries or sell them as rags.”
Thing is, what if they have lice? Yes, sometimes they have lice, blodd or other stains,
they aren’t worth cleaning, although maybe some do give to other countries.
I work for three thrift stores, no, we won’t sell the old stuff, we throw it out. Its not
worth the risk that it has lice or something in it. Old towels we use for rags though.
Clothes we don’t want to sell we give to another store. We now charge $25 to take tvs because
thats what it costs now at the dump for them.