Diamond color is the term used to refer to the hue a stone exhibits in light.  Diamonds come in a large variety of colors, but it is the saturation of that color that determines their value.  For example, although yellow diamonds are very valuable, a yellow-ish diamond can be nearly worthless.  

   

 The Diamond Color Grade

D, E, F      Virtually Colorless
G, H, I       Show Slight Color
J               Show Color (Not recommended)

Completely colorless diamonds are very rare and expensive.  Thankfully, slightly colored diamonds (G,H,I) usually appear colorless to the naked eye and can better fit your budget.

Keep in mind that lower grade diamonds can be adjusted using settings and cuts that show off the more colorless aspects of the stone.  If you're thinking about an emerald cut, be aware that the large table area will show off more color than any other cut.  Only D, E, F (and exceptional quality G) diamonds are recommended for emerald cut stones.  

Diamond Florescence:
Florescence in a diamond is similar to a white shirt under a UV light.  If your diamond does exhibit this rare phenomenon, blue florescence is the best choice for a colorless diamond.  
Blue florescence is complementary to diamonds with a yellow tint.  The blue makes the diamonds appear whiter and more colorless.  Orange or yellow florescence only work well with similar colored diamonds.  They are not desirable for colorless diamonds. 

Too much florescence can also be a bad thing, causing the diamond to look cloudy or oily.  Florescence also alters the diamond's brilliance depending on direct and indirect sunlight.  

Diamond color and different colored diamonds should not be confused with one another.  Colored diamonds are referred to as "fancy diamonds" and can come in blue, yellow, pink, champagne, brown and black.  The color in these stones is at such high saturation levels that a vibrant and undeniable coloring is apparent.  These stones are rare and expensive.

Tainted stones below the J color grade are often considered not suitable for use in jewelry and are used in the industrial world.