Generally, it is always a good idea to memorialize the terms of any agreement, including employment contracts, in writing. This helps avoid confusion, misunderstanding, lack of clarity in terms, and it also allows to not rely on their memory as to what they agreed on.
However, it is well established under California law that an oral agreement can be valid and enforceable. This is usually the case when the conduct of the parties suggests that they must have had an agreement about their relationship. For instance, if a worker is hired by his employer without signing any written employment agreement, a contractual employee-employer relationship is still created. The parties might later dispute the terms of employment (most commonly compensation and wages due), but if the employee presents evidence of performing work for the employer, statements from witnesses, and history of past compensation by the same employer, lack of written contract will not relieve an employer from his obligation to pay his employee wages and fulfill other applicable duties.
Still, certain contracts must be in writing in order to be valid under the “Statute of Frauds” exception. The most common such contracts are: (1) contracts for sale of goods for over $500; (2) a contract for services that will take one year or longer to perform, marriage, divorce, land sale transactions, and a promise to pay for debts of another (surety or loan guarantee).