Obviously you need auto and health insurance. It's even required by law. And, if you own your own home, you definitely want homeowner's insurance.
Now, let's look at a few other types of insurance.
Cell Phone Insurance: Perhaps you're the type of person who drops your phone constantly, or you have young kids, and you definitely need cell phone insurance. Consider paying your cell phone bill with a credit card that offers free coverage just for charging the phone bill to your card every month. (Of course, you'll want to be sure and pay the bill in full each month.)
Renter's Insurance: This one won't be the same for everyone. If you are a lifetime renter, and you have accumulated a lifetime worth of items, you probably will want to purchase renter's insurance. If you just moved out of your parent's home and everything you own is either curbside furniture or hand me downs, you might be just as well saving that money for your first home. Compare the annual cost with the amount you paid for your current assets.
Life Insurance: Obviously, if you are married with children, you will need to provide enough life insurance to not only pay for your funeral, but to provide the lifestyle your family is currently used to living. However, if you are single, you might want to consider planning your funeral and expenses in advance and skipping the monthly payment.
Life Insurance on a child: Put the money into a savings account for the kid instead!