Sometimes you have clothes that are nice that you just can't wear anymore, or never wore at all. Those are easy to sell, to gift someone else, or bring to a thrift store as a donation.
Things that are stained, ripped, that are tearing along the necklines - those will only be thrown out at the donation store, unless they have a downstream option for textiles. Most places don't, by the way. In this sense, your recycling efforts are wasted and you are making the thrift store bear the burden of your disposal needs. What makes me really cringe, though, is to think of developing countries where any fabric at all, any carelessly thrown away textile, becomes a source of potential income for poverty stricken rag-pickers. I wish I could just send my old clothes there!
Some donation stores do this: it's called downstream recycling. It's worth asking around in your community to find something like this.
Bear in mind that the next best solution is to simply use (and use again) your own textiles until they become truly unusable.
What to do with un-wearable old clothes?
I like to make rags of all kinds. When you consider that people go to places like Home Depot and spend their hard earned money on bags of rags, you will laugh and feel ahead of the game.
Soft tee shirt materials are good for house cleaning and dusting, and can be reused many times.
You can set some nice soft ones aside for gentle facial cleansing, or to wipe baby bottoms. I actually turn my old cotton flannel clothes into toilet wipes. They are soft, absorbent, and feel so much smoother on my bum than scratchy, expensive toilet paper.
Some rags (the less soft and absorbent ones) are best used once and tossed: rags for the workshop, for changing the oil in your car, washing your car, used in the potting shed, or with your paints and clay in the art studio. And used for dropcloths when house painting, fiddling with the furnace or wiping up pet mistakes. You can use these too, to clean the mud off your dog or the little wet feet of your cats.
Some old clothes are good to keep for sewing materials, for making patches, for stuffing into quilt work, plush toys or pillows, or ripping up to braid into rag rugs. Soft fleeces can be made into reusable menstrual pads - there are lots of online patterns for this.
Old pillow cases make great reuseable leaf bags.
Old fabric (even old carpet and carpet padding) can also go on the ground as a bottom mulch layer for gardening or weed control. Toss dried bark, gravel, or your 'pretty' mulch of choice right over the bottom layer of cloth.
Clothes made of cotton, silk and wool can even be composted.
Used woolen fabrics can be turned into felt.
Un-knit knitted items so you can reuse the yarn. You can get some really unusual and high quality yarns this way. Develop your creative eye when examining old knitted clothes, scarves and blankets.
Strips of fabric can be twisted into rag rugs, place mats, shelf liners, round cloth baskets, dog beds, welcome mats and just about anything your creativity can imagine.
Old ripped/stained (but clean) towels and blankets are gladly accepted by animal shelters to make bedding for their charges. I know I had a local thrift store that would save all the really old blankets for the asking to people with pets. When my cat had a litter one summer, I was able to get a whole bundle of throw blankets to make a birthing nest and kitten bed.
Give your old clothes and bedding some thought before tossing in the trash as unusable! Remember that in some places in the world, even the lowliest discard will be used many times until the fibers are worn apart.
There are also books on Amazon for the creative-minded to transform old clothes into unique new garments: New From Old: How to Transform and Customize Your Clothes and Rip It! How to Deconstruct and Reconstruct the Clothes of Your Dreams.