An adopted child has the same rights to inherit as do biological children; they also have the same rights regarding not inheriting. The fact is that a parent may disinherit their child. As a general rule, children have no right to inherit anything from their parents.
That having been said, most states do have laws to protect against accidental disinheritance. In rare cases, a child may have a right to “elect against the Will” if it appears the parent did not know about a child or if the child was born after the Will was signed (to disinherit these latter children, there must be specific disinheritance language in the Will). Otherwise, if there is a Will and you're not in it, you are not entitled to any of the estate.