According to the Teachspin website http://www.teachspin.com/instruments/faraday/index.shtml, Faraday rotation has a practical application in optical isolators.
"An optical isolator is a device that allows light to go through in one direction but severely attenuates reflected light propagating in the opposite direction. Modern ultra-high field permanent magnets and special paramagnetic glasses have made these devices quite small, but not cheap (about $2K)."
Optical isolators are applied to optical fiber systems and audio signal switching. They "have important applications in telecommunications preventing reflected signals on fiber optic cables from producing unwanted signals. Isolators are important when lasers are used because reflected light can cause havoc with the operation of the laser itself."
Also, Faraday rotation is used to detect magnetic fields in interstellar space.
To do this, astronomers/physicists have to estimate the electron density of the space that they are examining, and sum up the cumulative effects of all magnetic fields (parallel to the propagation of the light) between the source and where the measurements of polarization are carried out, on Earth.
In interstellar space, the angle of rotation is proportional to the number of electrons that the light hits times the strength of the magnetic field (parallel to the propagation of the light) multiplied by (integrated over) the distance that the light travels in the field, divided by the wavelength of light squared. By comparing and analyzing the relative degrees of polarization at various different wavelengths, astronomers can map out magnetic fields far out in the universe! (At least what they were when the light passed through them, which could have been a very long time ago.)