This paper presents an analysis of refinement indicators for the simulation of steady and unsteady flows by means of p-adaptive algorithms for discontinuous Galerkin (DG) methods. Residual error, discretization-error and feature-based indicators are compared by studying their effect on convergence history, computational gain and refinement regions selected by the adaptive algorithm. The analysis is initially carried out on steady flow configurations. Static p-adaptive simulations of the periodic flow past a cylinder at Re = 100 are then performed. Compared to uniform p-refinement, a reduction between 50% and 75% in the number of degrees of freedom is obtained for all test cases considered. The accuracy and efficiency observed for the small-scale energy density and spectral decay indicators demonstrate their great potential for the adaptive simulation of unsteady flows.