As you read in the answers to the previous question, a Will provides a legal mechanism to transfer property that is required to go through a probate proceeding. The purpose for probate is to allow a court to appoint trustworthy executors, trustees, and guardians (hopefully the ones you chose in your Will if they can qualify), to ensure the payment of legally valid debts and taxes, and to supervise the orderly transfer of estate property to the rightful heirs. Many people believe probate is a long, arduous, and expensive process that must be avoided by use of some creative estate planning methods. Sometimes probate is all of these things and, is also a public proceeding which means that anyone who is interested in "who got what" can generally find out. But the critical part about having your own legally valid Will in the probate process is that your wishes as to appointment of fiduciaries and inheritance of property are generally followed by the court.
Probate property is, generally speaking, any property that does not already have a legal mechanism for transfer to someone else. Examples of property that typically do not go through probate are insurance policies with a designated beneficiary, joint bank accounts, retirement accounts with beneficiary designations, and real estate owned with a spouse or another person.
It is very important that you review your insurance policies, bank, brokerage and retirement accounts, and other "non-probate" property to ensure you know who will receive the benefits of these upon your death. It doesn't matter if you have a Will that directs some other result for these assets. These will simply never find their way into the probate process and the Will has no effect on their disposition.
What happens to other, probate, property, if you don't have a Will? Well, contrary to what many 
people think, the "State" doesn't take your money except in extremely rare circumstances. What really happens if you don't have a valid Will is that your State has one for you in the form of State laws of intestacy. Intestacy is a legal term that basically means "died without a Will." So, in effect, all of us have some type of Will, either one of our own choosing or one that follows State law. It is important to understand some critical differences between these two.
If you create your own legally valid Will your heirs will, in many cases, have to have your estate go through a legal proceeding called "probate." On the contrary, if you die without a Will and the State law of intestacy is used in the probate process, there may well be a very different -- and undesired -- outcome. The judge will appoint an "administrator" of the estate instead of an executor. Generally this is a local lawyer and not a family member. The administrator is in charge of ensuring that debts and taxes are paid, including his/her own fee as set by State law or regulation. The main distinction between having a Will and being intestate is who inherits your probate property. This varies by State. In some States a spouse gets everything if any children are also children of the marriage. This is the law in Virginia. Other States provide a spousal share and a child's share, even for children of the marriage. This is the law in Maryland, where the spouse gets 50% and the children get 50%. Other States have some variations on these inheritance schemes.
The bottom line -- you should review and update all of your beneficiary designations for non-probate assets. If you do not already have a Will the process for settling your estate can, and often does, lead to increased costs, delays in inheritance, and unintended consequences. A Will is the basic building block of any estate plan. Having a legally valid Will makes things significantly easier for your family at a time of great emotional stress. If you have a Will you provide your family and the court with guidance on what you want to happen with your children and your property. This is especially critical in second marriage situations with children of both marriages.
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