If you're backpacking or travelling with one bag, you'll have to learn to do laundry in hotel rooms, bathroom sinks, and other areas without a washer and dryer. A multiple-strand travel clothesline is great for drying as your clothing tucks between the strands so you don't need a clothespin.
You can buy one for around 10 bucks online but they're simple to make and only require around a dollar's worth of rubber bands.
Instructables user br3ttb used 60 rubber bands to make a travel clothesline by soaking the rubber bands in water to make them more pliable, separating the bands into three even piles and tying each pile into a long strand, and braiding the strands together.
The only trick with using the clothesline is hanging it up. You can wrap the entire clothesline around one object and run the rest of the line through the loop; pics of this are at the link below. Commercial clotheslines sometimes include suction cups, which shouldn't be hard to scrouge, but I think a cheap keychain carabiner would work better.
Make a Rubber Band Travel Clothesline (for Less Than $US1) [Instructables]