Yesterday I talked about putting wood chips into a chickadee box and watching the chickadee pair "excavate" the box. They do leave some of the chips in the bottom of the box and then cover the chips with soft fibers. I've seen moss in a chickadee nest, as well as fibers taken from a coir doormat and animal hair.
For years, I've put cat hair in an old suet cage to provide birds with an easy source of nesting material. I've also put out sheeps' wool and have had chickadees, titmice, even Purple Finches pull out wool to line their nests. I pull tufts of the material out of the cage so the birds have an easy start at it.
This year I've put out a new nesting material that we're carrying at Wild Birds Unlimited - an alpaca wool nesting ball. It is a bunch of multi-color real alpaca wool stuffed into a 5" grapevine ball. I hung one the other day from my APS decorative branch and it took only 1/2 hour for the chickadees to start pulling wool out for their nearby nest.
Black-capped Chickadee with a tuft of alpaca wool for their nest.
So why not consider putting out some natural nesting material for your birds - they'll put on a great show for you!