If you're rough on your shoes, then you've probably destroyed your share of laces by cracking the plastic around the tip and causing it to fray. Once this happens, it's a pain to rethread the lace. Instructables user lllshreelll shares a simple way to repair the frayed laces with nothing but glue, thread and toothpaste.
Start by dabbing the frayed shoelace tip in the glue, and then wrap a small piece of thread tightly around it. Let the thread dry for 10 minutes, and then coat it in toothpaste. The toothpaste seals everything together and, according to lllshreelll, it's a pretty durable fix.
Quick, Cheap, and Easy fix for frayed laces [Instructables]