Color

Corundum can be colourless, red, pink, blue, black, brown, orange, yellow, green, indigo, violet, or mauve. Red corundum and most pink corundum is called ruby, blue corundum is called sapphire, and other colours are also called sapphire, usually with the colour specified as a prefix to the word sapphire, for example, yellow sapphire.

Colouration

Pure corundum is colourless, often called white, and although quite rare, tends not to be valuable because it does not have much brilliance. Colours, as in many gemstones, are caused by small amounts of impurity, usually metallic oxides. This is a case where impurity is desirable.
Chromic oxide causes brilliant red colouring in corundum, thereby producing rubies.
Ferric oxide causes yellow colouration, titanium oxide produces vivid blue.
In fact the colouration of sapphire is not quite so simple as this. The titanium and iron are usually present in the form of ilmenite, a mineral which is a titanium iron oxide, TiFeO3. Ilmenite is not isomorphous with aluminium oxide. Isomorphous means being able to replace the host mineral within its crystal structure. Instead ilmenite is present as a microscopic inclusion, in the form of colloidal particles.
This colloidal nature may be responsible for other optical effects such as "silk", asterism, and colour banding.

The Best and Most Valuable Colour

We are frequently informed, by partially educated customers that the darker the sapphire the better. We are equally frequently and erroneously told the opposite. If you think, even briefly, about this it becomes obvious why. A very dark sapphire would appear black, and would not be very attractive or desirable. The darkness often being caused by inclusions. An extremely pale sapphire would be colourless, and although rarer than black sapphire, is not particularly attractive or valuable.
As usual, the truth lies between the two extremes. The most desirable sapphires are generally those with an intense blue colour, and plenty of sparkle and life. These latter two factors are usually helped by high optical clarity and skilful cutting.
Ultimately which is "best" is a subjective matter, and personal preference is important. Our usual advice to potential customers is to buy whichever colour of sapphire they personally find the most attractive. We also think it's slightly sad that we need to give this advice. Buy what you like, using your own judgment, rather than allowing yourself to be a slave to fashion and buying what you think will impress other people.