Plunging your face into a musty-smelling towel is a sure way to start the day off wrong. There are many causes of this stink, but all of them involve moisture and mildew or bacteria, and sometimes other factors. The cause may be in your house, laundry equipment or laundry products. Whether the problem is acute today or chronic over time, the best way to resolve it is to start at the source.
Towels live mostly in the bathroom, the most waterlogged room in a house. Many bathrooms don't have a window, so the moisture from baths, showers and the ever-present toilet has no place to go except into the towels hanging or stored there. To correct this, install a vent fan capable of doing a full air exchange in just a few minutes. Be sure it's vented to the outside. If the dirty clothes hamper lives in the bathroom, it's just adding fuel to the fire. Dry wet or sweaty clothes before putting them in the hamper, wash them promptly, and take the hamper out and set it in the sun for several hours at least once a week.
Towels that come out of the dryer or off the line with the slightest trace of dampness remaining will sit in the linen closet or hang on the towel rack, and grow mildew and bacteria. Check them while they are still warm, and check them again after they cool. If they're not bone dry, put them back for an extra 5 minutes or so.
Mold and mildew can live in your washing machine and give everything an off smell. Check around, behind, under and inside the washer cabinet (especially a front loader) for sweating pipes/hoses or minor leaks. Odours proliferate in dampness. Review he instruction book for the washer and the manufacturer's recommendations for cleaning it. If there are none, once a month add a cup of household bleach to a wash cycle (no clothes this time, just water) and follow that with a cup of white vinegar in the rinse cycle. Chlorine is a base and vinegar is an acid, and between the two they should eradicate any nastiness. They also neutralise each other, so later loads will not be affected.
Washing too many towels at once can cause a washer to rinse less than thoroughly, and detergent build-up attracts mildew. Wash fewer towels per load and consider a second rinse cycle that includes half a cup of either baking or washing soda. Using too much fabric softener actually can waterproof towels. If water and detergent cannot get into the fabric to clean it, the towel can't possibly be or smell clean. A cup of white vinegar in the rinse water will help get rid of build-up -- some homemakers wash towels regularly with vinegar only, no detergent, and the towels come out clean, soft and sweet-smelling.