Cuts for gemstones:

Asscher - A square emerald cut developed in 1902.

Baguette - A diamond cut, usually rectangular, but can also be tapered.

Brilliant - A 58 facet cut diamond. One of the most popular cuts today.

Cabochon - A cabochon is a stone that has a rounded, domed surface with no facets.

Emerald - A rectangular cut often used for emeralds (hence the name) but also for diamonds and other stones.

Marquise - A fancy "boat shaped" diamond cut. Oval, but with pointy ends.

Oval - Guess what shape?

Princess - A square-cut diamond equivalent to a brilliant cut. Also called a Quadrillion or Squarillion cut.

Radiant - A cross between a square emerald cut and a brilliant cut.