The SARS-CoV-2 virus is responsible for the current worldwide coronavirus disease 2019 (COVID-19) pandemic, infecting millions of people and causing hundreds of thousands of deaths. The Spike glycoprotein of SARS-CoV-2 mediates viral entry and is the main target for neutralizing antibodies. Understanding the antibody response directed against SARS-CoV-2 is crucial for the development of vaccine, therapeutic and public health interventions. Here we performed a cross-sectional study on 106 SARS-CoV-2-infected individuals to evaluate humoral responses against the SARS-CoV-2 Spike. The vast majority of infected individuals elicited anti-Spike antibodies within 2 weeks after the onset of symptoms. The levels of receptor-binding domain (RBD)-specific IgG persisted overtime, while the levels of anti-RBD IgM decreased after symptoms resolution. Some of the elicited antibodies cross-reacted with other human coronaviruses in a genus-restrictive manner. While most of individuals developed neutralizing antibodies within the first two weeks of infection, the level of neutralizing activity was significantly decreased over time. Our results highlight the importance of studying the persistence of neutralizing activity upon natural SARS-CoV-2 infection.