Organic waste has the potential to produce methane gas as a substitute for petrol-based fuels, while reducing landfilling and possible environmental pollution. Generally, anaerobic digestion (AD) is used only in wastewater treatment plants as a tertiary stage of sewage sludge treatment, generating a fraction of the energy that such process plants require. In this study, four different wastes—food waste (FW), dairy industry waste (DIW), brewery waste (BW), and cardboard waste (CBW)—were tested for biogas production. The biochemical methane potential (BMP) of each sample was evaluated using an automatic methane potential system (AMPTS). Operating parameters such as pH, temperature, total solids, and volatile solids were measured. Experiments on the anaerobic digestion of the samples were monitored under mesophilic conditions (temperature 37 °C, retention time 30 days). Specific methane yields (SMYs), as well as the theoretical methane potential (BMPth), were used to calculate the biodegradability of the substrates, obtaining the highest biodegradability for BW at 95.1% and producing 462.3 ± 1.25 NmL CH4/g volatile solids (VS), followed by FW at an inoculum-to-substrate ratio (ISR) of 2 at 84% generating 391.3 NmLCH4/g VS. The BMP test of the dairy industry waste at an inoculum-to-substrate ratio of 1 was heavily inhibited by bacteria overloading of the easily degradable organic matter, obtaining a total methane production of 106.3 NmL CH4/g VS and a biodegradability index of 24.8%. The kinetic modeling study demonstrated that the best-fitting model was the modified Gompertz model, presenting the highest coefficient of determination (R2) values, the lowest root means square error (RMSE) values for five of the substrates, and the best specific biogas yield estimation with a percentage difference ranging from 0.3 to 3.6%.