In a Priority Program on Massively Parallel Computing, eight Dutch research groups (http://www.phys.uu.nl/~mpr/) cooperate since 1995 to develop new algorithms and software to simulate the non-linear dynamics of thermonuclear, geophysical, and astrophysical plasmas. As one result of this collaboration, the general-purpose {\bf Versatile Advection Code} (http://www.phys.uu.nl/~toth/) has demonstrated excellent scaling properties across a variety of shared and distributed memory architectures. VAC uses various shock capturing numerical methods with explicit, semi-implicit, or fully implicit time stepping, on 1, 2, or 3 dimensional finite volume grids. Portability to different hardware platforms is achieved by preprocessors that can translate the code from Fortran 90 both forwards to High Performance Fortran and backwards to Fortran 77. With this code, we simulate complicated magnetized plasma phenomena where simultaneous large-scale and small-scale structures evolve on different timescales. We investigate fundamental hydromagnetic instabilities in multi-dimensional, fully non-linear regimes, as well as astrophysically oriented applications. An overview of recently investigated phenomena includes: the role of the magnetic field in Rayleigh-Taylor and Kelvin-Helmholtz instabilities, stellar wind models and solar coronal mass ejections, and accretion flows onto compact objects (black holes).