Many other animal species produce silk. Silk is produced by many species of bees, wasps and ants, often for nest construction. Most famously, spiders and other arachnids use silk to spin their webs.
None of these other species have been used for commercial textile production, though research continues into whether any such alternative to the silkworm might be viable. Already the silk from some of these other animals has been used in weapons and optical instruments such as telescopes.