Not all contracts need a witness. For example, a simple agreement between two parties likely will not need a witness, although it is in your best interest to have one. However, certain contracts will need a witness. For example, a deed or a will both need witnesses.
Just like wills, there is generally no requirement that a contract be notarized in order to be legally binding. However, if a party who signed a business agreement decides to dispute that agreement in court, a notarized contract can help a great deal.