A number of countries in the world have decided to set a minimum age of 18 or higher for both men and women, including China, Denmark, Egypt, Kenya, the Philippines, South Korea, Sweden, Switzerland, and Vietnam, among various others. (In some countries that officially do not recognize younger marriages they still take place.)
Most jurisdictions -- including all U.S. states -- still allow minors to marry with permission from one or both parents, the approval of a court, or both. For details by country, see this Wikipedia article. The rules for U.S. states can be found in this one.
Despite tradition, there's much to be said for preventing marriages by people too young to sign a contract or buy a house or car. In most places marriage is supposed to be a long-term commitment, and 17 or younger is pretty young to make a decision that could affect the rest of your life. True, some marriages to very young spouses are happy and enduring, the classic example being that of Will and Ariel Durant. (He was a teacher in his late 20s when they married and she was a student in her mid-teens. According to their autobiography, she had pursued him rather than the other way around. The Durants died two weeks apart in 1981 when he was 96 and she was 83. She had stopped eating when he was taken to the hospital and died first. His death came very soon after he learned of her death from a television news report.)
But most child marriages are not so romantic and the great majority end in divorce, at least when divorce is allowed. In many cases the woman is much younger than the man and not particularly interested in marrying him but is coerced into doing so. When both parties are relatively young, it's still pretty common for the marriage to follow pregnancy and to serve as a way to avoid a charge of child molestation or statutory rape.
Various groups and individuals have been trying to get the law changed. As Samantha Bee reports below, in New Hampshire, which now allows boys to marry at 14 and girls at 13 with the consent of a judge, a Girl Scout is leading an effort raise the marriage age to 18.