The easiest way to reuse textiles that have seen better days is to turn them into cleaning cloths. This can be great for messy spills and a more sustainable alternative to paper towels. Most fabrics can be cut up into large squares without too much fraying. Super absorbent fabrics like fleece are especially useful. Once you have mopped up a spillage you can just pop the fabric in your washing machine and reuse again and again.
Alternatively fabrics that are pretty or have sentimental value could be used in a craft project to give the item a new life. Patchwork blankets are an ideal way to display and repurpose old baby clothes or items of clothing from a family member that you want to remember.