The short answer is no. You have no legal obligation to include your children in any bequests or to name them as beneficiaries. There is, however, a catch.
If you do not have a will or a trust or any kind of estate plan in place when you die, the state of Ohio will distribute the entirety or a portion of your assets to your children. How much each will inherit depends on whether you have a surviving spouse and whether your spouse is also the parent of the children, but they may very well inherit.
Please note: In this context, Ohio defines "property" as both real property (real estate) and personal property (belongings). As a result, it is possible that your four children, together, will inherit your house, your car and your art collection.
The state will award your entire estate to your surviving spouse if you both are the parents of your children. Should your spouse predecease you, the estate would go to your children or their descendants in equal shares. Any children your spouse had that were not yours by birth or adoption would not inherit.
On the other hand, if your spouse survives you and you have a child that is not your spouse's, the formula changes. The spouse receives the first $20,000 of the estate and half of the balance; the remainder goes to the child.
That formula applies only if there is one child. If there are more, the division of the estate depends on whether the spouse is the parent of none or of one or more of the children. If the spouse is the parent of at least one of the children, he or she will take the first $60,000 and one-third of the estate. The remainder will be distributed among all of the children and their descendants. Now, if the spouse is not the parent of any of the children, the first $20,000 and one-third of the estate will pass to him or her, and the children will inherit the remainder in equal shares.
What this boils down to, then, is that the best way to control who will inherit your property when you die is to execute a will or create an estate plan. You need to make your wishes known.
Source: Baldwin's Ohio Revised Code Annotated, Chapter 2105: Descent and Distribution and Chapter 2106. Rights of Surviving Spouses, via WestlawNext