Sheet maintenance depends on sheet material. Typically, natural fibers are more durable and can stand up to machine washing and tumble drying better than synthetic materials. Cotton and wool sheets are both quite easy to maintain.
Even luxury sheets made of these fabrics are typically machine washable. Though it's a natural fiber, delicate silk is a little trickier. You technically can machine-wash silk, but you'll need to pay close attention to the care instructions. And you may have to hang silk sheets to dry.
Synthetic fabrics are usually tougher to maintain than natural fabrics. You can machine wash many synthetics – like microfiber and polyester – but not always. Tumble drying may also damage these fabrics. As with all textiles, read and follow the care instructions for maximum longevity.