Instead of throwing them out or throwing them to the moths, use them for things like home accessories and slippers.
Recycled Sweater Purse:

Image: pinterest
Cashmere Bunny Tutorial:

Image: betzwhite
Ear Warmer:

Image: maverydesigns
Sweater Flip-Flop Slippers:

Image: craftsy
Patchwork Messenger Bag:

Image: pinterest
Wintery Flower Pot Sweater Sleeve:

Image: acultivatednes
Doggie Slippers:

Image: typepad
Elf Hat:

Image: pinterest
Felt Slipper:

Image: craftsy
Sweater Wreath:

Image: sewsweetstitches.blogspot
Old Sweater Purse:

Image: pinterest
Sweater Boots:

Image: sew-whats-new