Heat pumps, an example of one of the most environmentally friendly technologies, can play a key role in the future of sustainable energy. Due to the European Union’s ambitious goals to achieve climate neutrality by 2050, research is currently focused on finding solutions to increase the energy and economic efficiency of heating and cooling with heat pumps to benefit the environment. This paper presents the results of energy simulations for a single-family building located in selected cities—Warsaw (Poland), Madrid (Spain), Riga (Latvia), and Rome (Italy)—as a case study for different climate conditions and energy policy. In each variant, ground and air source heat pumps are considered for heating, cooling, ventilation, and air conditioning (HVAC) purposes. Moreover, we conducted an economic estimation including investment and operating costs, as well as an ecological analysis of carbon dioxide (CO2) emissions. Results show that heat pumps as an energy source for HVAC systems seem to be much more beneficial for Mediterranean-type subtropical climates, than for continental-type climates. The lowest value of total energy demand was obtained in Rome (60 kWh/m2∙rok), while the highest values were recorded in Riga and Warsaw (more than 90 kWh/m2∙rok). In terms of economic and environmental aspects, the use of heat pumps was most advantageous when considering Rome. This paper provides a starting point for further research focusing on increasing the energy and economic efficiency of heat pumps, especially in cold climates, as well as a multi-parameter analysis taking into account national prices, policies regarding development of renewable energy sources, and technical and climatic conditions. It also shows how increasing the share of renewable energy sources (RESs) in the national energy mix contributes to the reduction of CO2 emissions.