There are very few states in the U.S. with legal minimum ages, but many state agencies have published guidelines (NH, Illinois, Maryland and Oregon are a few of the states with very specific ages). Typically 8 year olds and over can be left at home for up to several hours (usually after school before a parent gets home from work).
12 years old appears to be the most common recommendation.
Home Alone Children Age Limits provides a state by state comparison.