Cubic Zirconia, a transparent, singly refractive, man made gem produced from the element zirconium, is by far the most popular substitute for diamonds. This is partly because it is inexpensive to make. It's also very sparkly and fairly durable, with a Mohs hardness of 8.5 (diamonds, at the top of the scale, are 10; sapphires are 9).
Like naturally occuring stones, it varies in color. However, the most common color you're likely to find is a bright white that closely resembles what you'd expect from a diamond.
It is sometimes referred to as cubic zirconium, but I've been told* that's incorrect.
*Thanks, Professor_Pi (and Gritchka)!