Young Earth creationists: roughly 6000 years. Old-Earth creationists: would generally say that it's as old as what is believed in Evolutionary theory.

See also:

Is there evidence for Creation?

Can you show that God exists?

Seeing God's wisdom

Creationists can be styled as "Young Earth" Creationists and "Old Earth Creationists".
Young Earth Creationists believe that the world is literally only about 6,000 years old, based on a literal reading of the biblical Book of Genesis. They believe that species have not evolved, but were created much as we know them today.

Old Earth Creationists accept the scientific evidence that the world is immensely old, but say that evolution, if it occurred at all, was guided by "Intelligent Design".

Another way of categorising some Creationists is as either Cosmic Creationists, who see intelligent design because the laws of the universe are exactly what suits the evolution of human life, or Biological Creationists, who say that the universe is so uncongenial to life that life could not have evolved naturally.

For more information on creationism and other views on our origin, please visit: http://christianity.answers.com/theology/the-story-of-creation