Summary: Non-inf-sup-stable finite element approximations to the incompressible Navier-Stokes equations based on equal-order spaces for velocity and pressure are studied in this paper. To account for the violation of the discrete inf-sup condition, different types of symmetric pressure stabilization terms are considered. It is shown in the numerical analysis that these terms also improve stabilization of dominating convection in the following sense: error bounds with constants independent of inverse powers of the viscosity are derived. For proving the bound for the \(L^2\) error of the pressure the choice of a suitable initial approximation for the velocity is essential.