To be valid, a last will and testament must be legally executed. You must sign your will in front of two witnesses, who must sign the will in the presence of you and the other witness.
A notary might enter the picture if your state permits wills to be self-proving — which means that they can be admitted in probate court without the hassle of herding up witnesses to appear in court or sign affidavits verifying that the person who made the will seemed of sound mind when the document was signed.
In most states, this is accomplished when the person making the will and the witnesses all appear before a notary public and sign an affidavit under oath, verifying that all necessary formalities for execution have been satisfied. Perhaps this is where all the confusion about notaries and wills comes in — although it’s more likely that folks just assume that a document as powerful as a will should be notarized to somehow give it a more “legalesque” aura.