The vast majority of cancer occurs in people over 50.
However, some cancers disproportionately target people in younger age brackets. Hodkins Lymphoma, for example, especially affects people in their 20s and 30s. Brain and nervous system cancers seem to be more evenly proportional across all age brackets. Leukemias, while affecting every age bracket, are especially prone to affect young children from 0-4 years old.
Cancer, which includes a whole host of diseases that involve out of control cell replication, is definitely enhanced by age. Why this is true is not completely clear.
In many cases, such as lung or liver cancers, the accumulation of time often correlates with the accumulation of environmental toxins, which can increase the disruption of normal cell activity and lead to malfunctioning cells that replicate out of control. Cancers that target the young are less clearly related to environmental toxins, though that hypothesis (that environmental factors contribute to cancer in younger humans) cannot be ruled out completely.