Your need for life insurance changes with the stages of your life, starting with no need when you're young, progressing to greater and greater need as you take on more and more responsibility, and finally beginning to diminish as you grow older.
When you're single
Sad though your death would be, it's unlikely it would create financial hardship for anyone. Any honest financial assessment of your situation would have to conclude that you have little or no need for life insurance.
An argument could be made that you should buy a policy now while you're young and rates are low. And if someone -- a parent, say -- depends on you for financial support, then by all means, consider life insurance.
But consider the interest you could earn by saving and investing your money instead of spending it on insurance premiums. Still, if somebody -- a parent, a grandparent -- wants to buy you a policy now to lock in low rates for later in your life, accept it gratefully.
Love and marriage
Married couples with no children may need little or no life insurance, especially if both spouses contribute equally to the household income.
The death of either spouse would not be financially catastrophic; the other could presumably survive on his or her own income.
Still, it could be a strain. Perhaps the survivor couldn't afford the mortgage or rent payments on a single income, or maybe you have big credit card debts. Also, there would be funeral costs.
Each of you should probably buy a modest amount of life insurance to protect the other.
Married with children
A one-income family with young children is the classic high-need situation. Basically, all of these people are dependent on one breadwinner for their total support, so insurance on that life is vital. And if the nonearning spouse should die, the other would have to pay for child care -- a very expensive proposition that argues for insurance on both lives.
This same high-need situation exists for dual-income households with children, for single parents, and for those caring for elderly parents who have limited resources of their own.
The golden years
The kids have grown and are making it on their own. You have a pension and considerable assets that can be used to generate a good income after you die. In circumstances like this, you clearly don't need as much life insurance as you once did.
The one caveat here is estate planning. If your estate is large enough to be subject to the estate-tax when you die, your heirs can use the death benefit to pay the IRS. If the policy is held by a trust, the benefit would not be counted as part of your estate.
If you fall into this category, consider a whole-life policy. Since you don't know when you will die, you'll need to hold on to your coverage indefinitely.