In the U.S., although there is no law that states at which age parents can leave children alone, if a fire or other accident happens when children are left alone without supervision, the parents can be arrested and charged with reckless endangerment. According to Sharman Stein, New York City Administration for Children's Services' spokesperson, while some 10 year olds can be mature enough to be left at home, there are 14 year olds who haven't yet reached this level. Connecticut's Child Welfare Agency suggests that you wait until your child turns at least 12 if you want to leave him alone, and 15 years old if you want him to babysit his younger siblings.
Regarding teenagers left alone at night, concerns are safety issues from outside sources (strangers attempting to enter the house) and whether your teen will take advantage of your trust and throw a party in the house, invite a boyfriend/girlfriend to sleep over, or otherwise make problems for you. You should realize that you're legally liable for any damage or injury caused by a minor for whom you're responsible. How has your teen handled responsibility in the past? Does he come home when he says he will and generally abides by house rules? Is your daughter the type of teen who is afraid to disagree with her friends and follows along even when they suggest wild ideas?
Police in Berkeley, California, are summoned almost every weekend to close down out-of-control parties consisting of hundreds of teenagers and no adult supervision. These parties often feature alcohol, drugs, fighting and date rape. Although a teen may invite six or seven friends, once the word gets out that the house is parent-free, many uninvited teens show up as well. Unless you can convince a relative to sleep over and keep an eye on your teenager and your house, you may be better off waiting a few years until your teenager grows up before going away for a night or the weekend and leaving the house without supervision.