Generally, life insurance should be purchased if the death of the insured would cause a financial hardship. That's why parents of minor children need life insurance, so that there will be money to take care of the children financially if their parents die before they grow up. It's also the basis for those commercials with senior citizens talking about getting life insurance to cover their funeral expenses, so that their adult children don't have to pay for them.
On the other hand, you don't need life insurance if no one is dependent on you financially.
For instance, a homeowner who's single and doesn't have children probably doesn't need life insurance to pay off the mortgage in the event of death, since there's no surviving spouse who'd want to stay in the house, and the estate can sell the property to pay off the mortgage.
But if you've seen those Gerber Grow-Up Plan life insurance commercials, you may be wondering if should you buy life insurance for your children. In most cases, the answer is "no." The death of a child, while tragic, is statistically unlikely. Additionally, the death of a child rarely causes a financial hardship, at least after any expenses related to the death have been paid for. Thus, in most cases, a life insurance policy for a child would usually be considered as more of an investment vehicle. However, you could almost certainly get a better rate of return by investing the money in a conservative mutual fund. Or better yet, invest the money that would have been spent on premiums in a tax-advantaged vehicle like a 529 college savings plan. So for most families, life insurance for the kids just doesn't make good financial sense.
Of course, there are exceptions.
Some children actually do make money, especially out here in Southern California, home of Hollywood. Many such families focus on the child's career, and thus are dependent on the child's income. In that case, a life insurance policy may make sense, since the child's death would cause a true financial hardship.
Another exception would be if the child has some kind of condition that would make it difficult to obtain life insurance later in life. Policies like the Gerber Grow-Up plan are whole life policies, meaning they are good for the insured's entire life (as opposed to term life policies, which are only valid for a limited number of years). Thus, a child could carry a whole life policy for the rest of his life, even if he wouldn't qualify for a policy as an adult. Additionally, many whole life policies can be increased without medical testing when a child reaches adulthood.