When I learned about SOR, it was mostly given as one of the first examples of iterative methods, and then later the iterative methods that I would end up using would be Krylov subspace methods.Are any of the iterative methods like Gauss-Seidel and SOR ever used in practice? Do you know of any real packages that use them seriously, for something other than demonstration purposes?
Gauss-Seidel, SOR in practice?
linear algebra
Yes, but not as stand-alone solvers for linear systems of equations.  These days, they are used as smoothers in multigrid or as preconditioners in krylov methods.