Safety and Security is a great reason for opening an account at a bank.  If your money is in the bank then it is safe from theft or loss. Your money is also insured by the FDIC for up to $100,000.  There are a few other good reasons to open an account.

Using a bank can be much cheaper than going to another business to cash your checks.  A bank may charge you a monthly service fee to take care of your account, but a check-cashing service will charge you a fee for each check you cash - and that can add up to a lot of unnecessary fees. 

Your financial future is another good reason to use a bank.  Saving in a bank will allow you to accumulate safely the money you will need to buy a home, a car, or any other large purchase. Also, if you need a loan to make the purchase your bank account history will help secure a loan by demonstrating to the bank that you are financially responsible. 

Finally, there's Convenience.  A bank is convenient since it may have many branches and locations where you can go to deposit and withdraw your money.  Banks also offer time-savers like direct deposit and an ATM card or debit card, which means you don't even have to go to the bank to get your money in or out.