Sheets: every one to two weeks. Bath towels: after three or four uses. Pillows: twice a year. Those are the short answers. The longer answer depends on how much you sweat, whether pets sleep on the bed, and whether anyone in the house has allergies or is sick.

Every night you leave behind sweat, body oil and skin cells. Over a week or two, that builds up into food for dust mites and gives sheets that slightly sour smell. If you or anyone in the house has allergies or asthma, weekly washing makes a real difference. So does washing after anyone has been sick.
Wash sheets and pillowcases in the warmest water the care label allows; for most cotton sheets that's warm or hot. To kill dust mites the water needs to be at least 130°F (54°C). If your linens can't take that, a hot dryer cycle helps too. Towels do well in warm or hot water. Skip fabric softener on towels; it coats the fibers and makes them less absorbent. A half cup of white vinegar in the rinse cycle softens them without the coating.
Most polyester and down pillows can go in the washer. Wash two at a time to keep the drum balanced, on a gentle cycle with a small amount of detergent and an extra rinse. Dry them on low heat with two clean tennis balls or dryer balls to break up clumps, and make sure they're completely dry inside before putting them back on the bed. Memory foam pillows should not go in the washer; spot-clean and air them out instead. Replace pillows every one to two years, or when they stay flat after fluffing.
A queen or king comforter often won't fit in a standard home washer. Using a laundromat's large-capacity machines is cheaper than dry cleaning and works well for down and synthetic fills. Check the label, use a gentle cycle, and dry on low with dryer balls until there's no clumping or dampness left.
Keep two sets of sheets per bed so one can be washed while the other is on. Strip the bed in the morning, wash, and remake it the same day. Our weekly cleaning schedule puts sheets on the same day every week so it stops being something you have to remember.
Every one to two weeks. Wash them weekly if you sweat at night, share the bed with a pet, or anyone in the home has allergies, and after anyone has been sick.
After three or four uses, as long as they dry completely between uses. Wash them sooner if they stay damp or start to smell. Washcloths should be washed after each use.
About every six months. Most polyester and down pillows can be machine washed on a gentle cycle and dried on low heat with dryer balls. Memory foam pillows should be spot-cleaned instead.
Water of at least 130 degrees Fahrenheit (54 degrees Celsius). If your linens can't be washed that hot, a hot dryer cycle also helps.