Rarefied gas flows in channels, pipes and backwards-facing steps are studied in a wide range of Knudsen number (Kn) with the objective of developing continuum-based simplified models. Such flows are encountered in micro-electro-mechanical-systems (MEMS) and in low-pressure environments. A new general boundary condition that accounts for the reduced momentum exchange with wall surfaces is proposed and its validity is investigated. It is shown that it is applicable in the entire Knudsen range and it is second-order accurate in $Kn$ in the slip flow regime. Firstly, channel and pipe flows in the slip flow and transition flow regimes are simulated using the DSMC method. Corresponding spectral element discretizations of the compressible Navier -Stokes equations subject to various slip models are also performed for Kn<1. DSMC based solutions as well as solutions of the linearized Boltzmann equations are used to test the accuracy of the macroscopic models. A universal scaling for the velocity profile is obtained, which is used to develop a unified model predicting the mass flowrate with good accuracy in the entire flow regime (0 < Kn < oo). A rarefaction coefficient is introduced into the model to account for the increasingly reduced intermolecular collisions in the transition and free-molecular regime. This model also predicts correctly the well known Knudsen's minimum in the transition flow regime as verified by experimental results and the DSMC data. Secondly, the effect of rarefaction on separated flows is studied by considering the backwards-facing step geometry in the slip flow regime. The multiple length scales and the sudden change in rarefaction conditions at the step expansion introduce substantial complexity in this case. First- and higher-order slip boundary conditions are employed in the continuum simulations and the results are compared against corresponding DSMC simulations. Good agreement is achieved suggesting that the more efficient continuum-based approximations are valid in the slip flow regime even for separated rarefied flows.