The European Union, in accordance with its decarbonization objectives, has enacted the Directive (EU) 2018/2001 and subsequently the Directive (EU) 2019/944 that legally recognizes and regulates the formation of citizen energy communities. These are believed to be key enablers for reducing buildings’ carbon footprint by allowing for a wider diffusion of on-site renewable energy generation and by maximizing renewable energy self-consumption. In this study, the benefits of the energy community are assessed through simulations of average Italian buildings of various sizes, different energy efficiency levels, equipped with a photovoltaic system and a heat pump-driven heating system, and located in heating-dominated climates. The work focuses on energy communities both at the apartment scale—i.e., in a multi-family building—and at the building scale—i.e., in a neighborhood. The net energy consumption, the self-consumption, and the self-sufficiency of all the possible energy communities obtainable by combining the different buildings are compared to the baseline case that is represented by the absence of energy sharing between independent building units. The energy community alone at both the building-scale and the neighborhood-scale increases self-consumption by up to 5% and reduces net energy consumption by up to 10%. However, when the energy community is combined with other maximization strategies such as demand-side management and rule-based control, self-consumption can be raised by 15%. These results quantify the lower bound of the achievable self-consumption in energy communities, which, in the rush towards climate neutrality, and in light of these results, could be considered among the solutions for rationalizing the energy consumption of buildings.