Why do the lines on paper fade (and eventually disappear) if left in sunlight?

Ultraviolet light (which sunlight has plenty of) can ‘bleach’ the paper by slowly breaking down various inks and pigments.

http://en.wikipedia.org/wiki/Ultraviolet_light#Degradation_of_polymers.2C_pigments_and_dyes

also construction paper looses its color… i guess any paper

The line faeries come and use them to build nests.

Given enough time the sun bleaches out a lot of things. Colored fabrics fade, too. Even my hair does to some extent. In the winter, when the sun is blocked by clouds, my hair is a dark, dark brown. In the summer, however, the sun bleaches parts of my brown hair to an auburn/copper color. People ask me every summer if I dyed my hair – every summer I say no and tell them it’s from the sun.