For underwear and socks, agree with the towel rack and heated towel rack (just wash them out in the sink every night or every other night, then let them dry on the rack). I use the shampoo provided by the hotel to do the laundry (one less thing to pack).
Items like jeans, slacks, sweaters, and skirts are carefully chosen and made of materials that don't absorb odors, and therefore don't require washing that often. When they do I bite the bullet and send them to the hotel laundering service at a trusted hotel.