Diamonds are among the most useful of gems in the game, very popularly socketed in shields for the resistance bonus.
Diablo III Diamonds
Diamonds are not found in Diablo III. Only Rubies, Topazes, Emeralds, and Amethysts are found in D3C, though other gem types might return in expansions. See the Diablo III wiki for more details.
Diablo II: Lord of Destruction
The following bonuses are provided by socketed Diamonds in D2X.
Diablo II Classic Stats
Diamond stats in D2C were slightly lower than they are in the expansion.