Suppose a husband has a wife and two minor children, if he were to die without a will, he would probably be shocked to learn that, in many states, his wife would only receive one-third of his probate property. The other two-thirds would go to the children under the intestacy laws.
Suppose a widow leaves two children, one healthy child and one with a physical handicap. A will could recognize the greater needs of the handicapped child, but the intestacy laws will treat the children equally.
Suppose that Aunt Martha would like a keepsake to go to her favorite niece. She can accomplish this by a Will, but the intestacy laws would not recognize Aunt Martha's intentions for specific assets.