This paper deals with various aspects of edge-oriented stabilization techniques for
nonconforming finite element methods for the numerical solution of incompressible flow
problems. We discuss two separate classes of problems which require appropriate
stabilization techniques: First, the lack of coercivity for nonconforming low order
approximations for treating problems with the symmetric deformation tensor instead of the
gradient formulation in the momentum equation (`Korn`s inequality`) which particularly
leads to convergence problems of the iterative solvers for small Reynolds ($Re$) numbers. Second, numerical instabilities for high $Re$ numbers or whenever convective operators are dominant such that the standard Galerkin
formulation fails and leads to spurious oscillations. We show that the right choice of
edge-oriented stabilization is able to provide simultanously excellent results regarding robustness and
accuracy for both seemingly different cases of problems, and we discuss the sensitivity of the
involved parameters w.r.t./ mesh distortions and variations of the $Re$ number. Moreover,
we explain how efficient multigrid solvers can be constructed to circumvent the problems with the arising `non-standard` FEM data structures, and we provide several examples for the
numerical efficiency for realistic flow configurations with benchmarking character.