While I would like to make a comprehensive list (in one go), this involves quite some research.

Please add in the comments if I miss something.

Subframe Supported

• FCurves (and anything they animate)
• Drivers (including the frame variable passed into PyDrivers)
• Shape Keys (Mesh/Lattice/Curve)
• Shape Keys (Mask)
• Curve/Path constraint.

Subframe Unsupported

• Movie/Image sequence.
• Fluid-simulation
• Smoke-simulation
• Video Sequencer
  Note that while its possible to access sub-frames via the Speed-Effect.
  Exporting subframes from the sequencer it's self is not supported.

Note:

In some cases if subframe support isn't working where it should be- this should be reported as a bug.