Generally there are two big categories; you are planning for other people or you are planning for yourself.
Insurance For Them
If I die earlier than I thought, I would want to make sure my parent, spouse and kids not to worry too much about immediate living expenses.If I suffer from heart attack, I don't want my spouse to use up all his money to cure me.If I am ill and cann't work for a long time, I want to make sure my kids still get paid for their pocket money.
Insurance For Me
If I lost my kidney, I don't want to use my own money for cures.If I am hospitalized, I want to live in good care private room but I want other people to pay for that.
Generally you can lump some reasons together to buy an insurance but it should sperate these 2 categories. If one of your insurances is for you yourself AND also your family, most often you will use up the amount and still leave nothing to your family.
Typical under-insured cases occur in disability and illness. When you are diable or critically ill, should you use the insurance money to cure for yourself or should the money be left for your loved ones ? If you care about your family, most of the time they will use the money on you instead. Like wise, may be a simple small cure can be done with your condition but all of your family members want to keep the money with themselves. Either way, you should be very clear and seperate your insurance plans for others or for youself.
This is especially important in overlapping coverages like accidents, followed by permanent disability and critical illness.
Death pay out is pretty for other people while medical plans are pretty much for ourselves.