Round Brilliant - Do not confuse with round. The round brilliant is the modern version of the round which has been refined for maximum shine. The round brilliant is by far the most popular and has the best angles to create the best shine and brilliance.
Princess - A square cut diamond that has refractive properties almost near round brilliant. The princess is the preferred square cut shape over radiant.
Oval - Not as popular for solitaires, but very popular for three stone anniversary rings, with two matching diamonds on the sides.
Emerald - A more traditional shape, the emerald is not as popular as it once was, but has an old world elegance to it.
Radiant - Popular before the princess shape was around, the radiant has more facets than a princess, but has the corners trimmed like the emerald shape.
Marquise - Like the emerald, the marquise is a traditional shape. This is probably the fourth most popular shape behind the round, princess and oval.
Pear - Mostly used in pendants, the pear shape diamond is shaped in a tear drop shape and has fairly good proportions to refract light well.
Heart - Hard to find due to low demand, but some people prefer a heart shape diamond for sentimental purposes.