You can name almost anyone as a beneficiary to your will. A related question to who can be included as a beneficiary is who must be included in your will.
People have many reasons for not including people in their will, leaving people token amounts, or expressly disinheriting them. Some of these reasons have to do with anger and hurt feelings, but often times, the reasons are not so negative. For example, sometimes a parent will disinherit a child who is successful in order to help a different child who is not doing as well.
While you have a large amount of freedom on choosing who is and is not in your will, there are a few restrictions on who you can disinherit in your will. The main restriction on disinheritance is on disinheriting a spouse. All states have laws that prevent a person from completely disinheriting their spouse. NY & NJ does this through a device called an elective share. An elective share allows a spouse to choose between accepting what was left in the will, or alternatively, accepting a percentage of the estate that is determined by state law. The law adjusts the total value of the estate to account for assets that you previously transferred out of the estate by means other than by will.
There are no specific laws in any state except Louisiana that specifically prevent you from disinheriting a minor child. However, the probate court will often step in and use the assets of your estate to provide support to your minor child.
In both NY & NJ, a will maker can disinherit their adult children, parents, siblings, extended family, etc. Depending on your relationship with the person and the size of your estate, the way you disinherit can lead to bad feelings and potential will contests. There are probate laws that courts use to prevent a will maker from accidentally leaving their children out of their will. As a result, if you want to disinherit an adult child, you should do it explicitly.
If you decide to disinherit someone, it is often best to talk to your family about your wishes. These conversations can be difficult to have, but they can often prevent misunderstandings, hard feelings, surprises and will contests in the future.