Do all employees need to have employment agreements?

No. New York and New Jersey are both at-will employment states, meaning that your employer can terminate you for any reason, absent an illegal reason, and you can leave that employer for any reason without recourse. The people that have employment agreements are usually executives or union employees that are governed by a collective bargaining contract. If you could get an agreement from your employer that governs the compensation, the reasons that they can terminate you and there in black and white, that’s the best thing to have, but most employers don’t offer them. Again, if you can get a contract, great. If you can’t, most people operate under the at-will doctrine.