For a group of threads bundled together:
* A skein of thread
* A spool of thread
* A ball of thread
* A hank of thread
* A bundle of thread
* A coil of thread
For threads in a particular context:
* A tapestry of threads (for threads woven together)
* A web of threads (for threads forming a network)
* A tangle of threads (for threads that are knotted or tangled)
Ultimately, the best collective noun will depend on the specific situation and the desired effect.