What software do movies use for FX?
There are a number of different options.  Some production companies use their own proprietary, in house systems for rendering.  There are a large number of companies that use existing commercial products however.  Maya, SoftImage, 3D Studio Max and Cinema4D are some of the big ones.  I have not personally worked with Cinema4D, but I know that physics simulation is possible in all of the first 3.  Cinema4D also supports physics simulation according to comments, though I have not personally used it.

It is also worth noting that a combination of both physics simulation and physical modeling can be used.  For complex systems like particle effects and such, simulation is pretty much the only option, but for some larger actions, they may actually film a movement and then animate it to match what they record.  This can either be automated (using motion capture where they tracks dots on an object from multiple angles and computers reconstruct the motion) or by an animator manually watching the video and reproducing it.

These models and scenes are then rendered using a process called ray tracing.  Ray tracing works by having a simulated view point and a simulated screen.  The image is formed at the simulated screen by sending a ray from the view point, through the pixel on the simulated screen and then allowing the reflections to be traced back until they reach light sources.  This produces highly accurate reflections and lighting effects but is much more time consuming than the kind of rendering used in 3d games.

The output of the ray tracing is then combined with other information (such as depth and transparency) that comes out of the 3d rendering engine.  This information is all fed in to a compositing program such as Adobe After Effects or Autodesk (formerly Discreet) Inferno.  These programs combine the 3d elements back with the actual video elements and allows for filters and effects to be applied to help blend the layers together smoothly.