A famous bearer was Jesse James (1847-1882), an American outlaw who held up banks and stagecoaches. He was eventually shot by a fellow gang member for a reward. Another famous bearer was the American athlete Jesse Owens (1913-1980), whose real name was James Cleveland (or J. C.) Owens.
This name was very popular in the English-speaking world at the end of the 19th century. Though it declined in use over the next 100 years, it staged a successful comeback at the end of the 20th century. The American sitcom Will and Grace (1998-2006) may have helped, though the name was already strongly rising when it premiered. It was the top name for girls in England and Wales in 2006.