The Alpine Butterfly Loop is an ideal knot to use for hanging laundry on a kite line or tying off to an anchor. It is a strong knot, keeping over 90% of the stregnth of the line. It is also very easy to untie even after being under considerable strain.
Animated view of how to tie the Alpine Butterfly Loop.
WikiHow - how to tie.
This next is way too much information, but if you are knotty like me, this Butterfly Bend is a terrific way to join two lines.