In this work, reduced order models are presented for fluid flows characterized by different Mach numbers, ranging from low-speed, highly viscous fluid flows to weakly compressible flows. To populate the initial database of high-fidelity solutions, a high-fidelity solver based on the discontinuous Galerkin method was used, given its capability to deal with both fluids at low Reynolds and convection-dominated problems. Two distinct approaches, depending on the type of equations -either compressible or incompressible- which are solved at the full order level, were used to enhance the stability of the resulting reduced order models. Both aforementioned approaches rely on the proper orthogonal decomposition and on the manipulation of the governing equations when projected onto the reduced space. Specifically, these manipulations consist of ⅰ) the enforcement of the Poisson pressure equations when incompressible solvers are used, and ⅱ) the linearization of the governing equations when compressibility is kept into account. Test cases of the proposed methodology are presented, carried out on both internal and external flows.