If you've ever used a laundry service offered by a hotel, then you know that it's rather expensive. You can save yourself money when traveling by simply hand-washing your own clothes.
Buy a small, travel-sized bottle of washing detergent that is meant for hand-washing, and wash your clothes in the hotel sink or bathtub. Wring them out really well, and leave them to dry in the shower or over the radiator (just make sure it's not still so wet that it's dripping).
Tide and Woolite are two well-known brands that offer laundry detergent for hand-washing in these convenient travel sizes, so they won't take up much room in your luggage.
On a related note, it also helps to bring clothes that can easily be hand-washed. Jeans and bulky sweaters will take a long time to dry, but lightweight clothes will do just fine.
