First off, the T-shirts. Even if they're worn through in areas, or the elastic has gone, they can still be turned into T-shirt yarn for other purposes. There are plenty of online tutorials on how to do this. My favourite is from Mollie Makes. Ignore the bit about needing a T-shirt without side seams – for most purposes, it doesn't really matter if your yarn includes seams.
At the moment I'm making a mat, but I could just as easily knit, or crochet the yarn into something else such as a bag or even a new garment. Again, there are oodles of tutorials and ideas online – you can start here with Pinterest.
I also have a pile of long, thin strips, mostly of denim, leftover from a quilt I'm making from repurposed jeans. I have plans for weaving these, but they're a little way down the 'to-do' list at the moment.
Last, but not least are the tiny scraps – too small for making anything useful – along with the thread offcuts, yarn ends etc that are the detritus of making. These, I'm turning into thread beads. The pic below shows the ones made mostly from the leftovers of my exhibition quilt – 10c piece for scale.
Newsweek article that I found via The Fringe Association (the blog of Slow Fashion October's founder, Karen Templer).