If you have any form of financial responsibility to some one else, it is likely that you will need life insurance.
There are some exceptions. If you have no debts, own your house out-right, or if you have a large amount of savings or other significant sources of capital or income that could be called on by your beneficiaries in the event of your death, life insurance may not be as necessary.
If you're particularly wealthy you may still require life insurance as a strategy to reduce the impact of inheritance tax for your beneficiaries
In most cases, the minimum amount of life insurance that should be in place should be enough to settle any outstanding debts and cover funeral costs. The amount of life insurance you need depends entirely on your own personal circumstances.
It's generally considered that if you have anyone, especially dependants, who would be financially disadvantaged by your death - i.e. by having to sell your family home due to the inability to keep up mortgage repayments, or would be liable for the cost of bringing up your children, - life insurance should be a high priority for you.