Yes, some fancy colored diamonds are extremely rare and very beautiful. Thus they tend to be more valuable and expensive than many others.
Diamonds come in all colors of the rainbow. The most valuable tend to be the blue, green, reds and pinks, depending on the purity and intensity of the color; but within the non-fancy color range those that are colorless are the rarest and therefore the most expensive.
Natural diamond were formed billions of years ago from carbon in the depths of the earth. In most instances other minerals or gases became part of the transformation process that turned the pure carbon into the unique crystal we call diamond. Within these minerals and gases were elements that resulted in varying degrees of color becoming apparent, the most common of which is a yellow tinge caused by the presence of nitrogen in the gem. Blue diamonds are usually caused by the presence of boron at atomic level, pinks and browns by plastic deformation and greens by radiation.