Mildew is a type of fungus that thrives in a warm, moist atmosphere. Although many synthetic fabrics are mildew-resistant, the most common types of fabric for it to grow on are cotton, linen, rayon, silk and wool. Mildew grows best where there is limited airflow, so if an item such as a pillow or stuffed animal becomes moist, the stuffing can often develop that telltale odor that means something nasty is growing in there. Luckily, there are a few things you can do to get rid of the fungus.
Throw any washable pillows or stuffed animals in the washing machine. Use the hottest water that the fabric can stand, as heat is what kills mildew.
Dry all washed items in the dryer on the hottest setting, checking them periodically to make sure the heat isn't damaging them. You can use the dryer's heat to kill the mildew in non-machine washable items, too.
Soak stubborn items in a bucket filled with water to which you've added a cup or two of white vinegar. Liquid (non-powdered) bleach is even better at killing mildew, but should only be used on all-white pillows or stuffed animals.
Spread towels or sheets out in the back yard. Place any really delicate items on the towels or sheets and let them soak up as much sun as possible. Sun isn't as effective at killing mildew as the heat from a dryer would be, but some items are too fragile to withstand harsher methods of cleaning.
Re-stuff the pillows or stuffed animals as a last resort. Open up a seam in a place where it will be least visible, then remove the mildewed stuffing and dispose of it. Replace the stuffing with new, synthetic stuffing for a more mildew-resistant toy or pillow.