The primary purpose of life insurance is to protect your dependents financially when you're gone. By the time you reach retirement, it's unlikely that you'll have many people depending on your income, so why would a retiree want a life insurance policy?
Before delving more deeply into this question, let's take a quick look at the different types of life insurance policy kicking around the marketplace today. The two most common types of life insurance are term life and cash value. Term life is a "pure" life insurance policy: You pay monthly premiums over a set term, and if you die at any point during that term, your beneficiary gets a cash payout. Cash value (which may also be called "whole life" or "variable life," depending on how the policy is set up) combines life insurance with an investment component: Part of your premium goes toward financing the policy's death benefit, while the remainder goes into an investment account that you can either cash out before your death or leave for your beneficiaries.
Just about everybody is better off sticking with a term life policy, rather than one of the cash value variants. First, the insurance component of cash value policies is generally more expensive than that of term life. And second, fees and commissions chew up such a large portion of a cash policy's investments that they'll nearly always perform more poorly than investments in an IRA or even a standard brokerage account.
Term life for retirees
In some cases, retirees may still have one or more financial dependents. You might have a spouse with no income or a disabled child, in which case keeping your term life policy makes a great deal of sense.
Retirees without dependents have much less reason to continue with their life insurance policies, though there may be exceptions. For example, retirees with a ton of debt might be concerned about passing that debt load along to their children after their death. In that case, they may opt to purchase a life insurance policy that will provide a big enough payout to take care of any remaining debts and perhaps give their children a small inheritance as well.
Life insurance can also provide a way for the affluent to avoid estate taxes by placing the policy in a special trust. The cash payout from a term life policy is exempt from federal income taxes, so by putting your money into the premiums while you're alive, you can provide your children with a tax-free inheritance after your death.
Choosing the right policy
If you decide that life insurance makes sense for you even after retirement, it's important to choose your policy wisely. First, you've already seen why term life is nearly always the best type of policy to choose. As a rule of thumb, the fancier a policy is, the more fees and commissions you'll have to pay, so stick with the simplest possible policy.
One exception for retirees would be a life insurance/long-term care hybrid policy. These policies combine coverage of long-term care expenses while you're alive with a death benefit for your beneficiaries after you're gone. If you're fortunate enough to never need long-term care, at least you know that some of your premiums from a hybrid policy will be put to good use in said death benefit. And such a hybrid policy may be cheaper than buying separate life and long-term care insurance policies.
Whichever type of life insurance policy you get, look for one with a fixed, or level, premium. Rising premiums can soar dramatically as you get older, leaving you with no choice but to cancel the policy. And the older you get, the harder it will be to get a new (affordable) life insurance policy.