Do employees and employers have to sign any kind of contract/agreement upon hire?

Dear Sir or Madam, I have a question regarding my employment and I don't know who to ask. Can you please help me? I was hired on W-2 (paid hourly) and the employer did not have me to sign any contract, except the papers for W-2 and my bio info. When I asked him if we should be signing anything, he said "no". I worked in the company for 2 days and could not work anymore due to the family matters. I called him to notify about that and he became very angry. He said that I should have given him the notice. Can you please tell me if he was right? Shouldn't we have signed some kind of agreement/contract upon hire or it is not mandatory? If not mandatory - how can i be sure that he is going to pay me the agreed hourly rate then? There would be no way, right? Also - can I request my employer to pay me for the hours that worked in 2 days? Thank you very much for your time.