No. You do not have to leave assets of your estate to your children or your spouse; however, if either exist, regardless of whether you leave them anything, you should mention them in the will. Otherwise they may file a claim against the estate arguing that you simply forgot them.
Although you need not leave anything to your spouse in your will, if you don’t, he or she will likely have the right to file a claim against your estate based on what’s known as the “elective share”.  State elective shares vary, but usually range between 1/3 and 1/2 of your assets.  In determining the amount of the elective share, some states only include those assets passing under your will (“probate assets”) while others include non-probate assets as well.