Do all contracts have to be in writing?

No, a contract does not have to be in writing.  A simple oral agreement is probably a legally binding contract. 

However, in certain cases no court action can be brought unless the promise or agreement is in writing and signed by the party to be held to the contract. 

Examples:

• A promise to answer for the debt, default or miscarriage of another person.
• A contract to sell, or a sale of, goods in the value of $500 or more, unless the buyer actually receives and accepts part of the goods or gives something in part payment for them.
• An agreement which is not to be performed within one year.
• A lease agreement for a period longer than one year, or contract for the sale of real property or an interest in real property.
• An agreement authorizing or employing an agent or broker to purchase or sell real property for compensation or commission.
• An agreement to bequeath any property, or to make provision for any person in a will.