<p>We investigate the general plasma–vacuum interface problems for the ideal incompressible MHD equations with or without surface tension and prove their nonlinear local well-posedness in standard Sobolev spaces under either non-zero surface tension or the stability condition that the magnetic fields are everywhere non-collinear on the interface. In particular, the results show that both capillary forces and tangential magnetic fields can stabilize the motion of the plasma–vacuum interfaces. Moreover, the vanishing surface tension limit results are established under the Rayleigh–Taylor sign condition or the non-collinearity condition. All these results hold with no graph assumption on the free interface.</p>