Crimes that incur capital punishment differ in each jurisdiction. Treason can be a capital offense, as can aggravated kidnapping, depending on the area in which the crime takes place. In states that exercise capital punishment, the most heinous forms of murder are considered capital crimes, such as murdering an officer of the law.
Some crimes can lead to a capital punishment verdict from a federal court, no matter in which jurisdiction they occur. These include certain grades of murder, treason or espionage, kidnapping across state lines if the victim dies and large scale drug trafficking.
Understand that capital punishment is not always imposed. Just because a person is convicted of a capital crime doesn't necessarily mean he will receive the death penalty. Capital punishment is the maximum sentence for such crimes, but there are lesser sentences as well. Usually a jury will review the case and determine whether there were any aggravating circumstances that would warrant the death penalty or mitigating circumstances that would warrant a lesser sentence.