Using LC filter instead of RC filter in mains powered circuits
Ideal capacitors and inductors don't dissipate any power, whereas resistors do.  One advantage is therefore that L-C filters are more efficient than R-C or R-L filters.  Often it's not the actual waste of power that is the driving factor, but the mechanics required to get rid of the heat.  Lamp dimmers often need to fit into small spaces where keeping them cool would be difficult.

Another advantage is that L-C filters attenuate more in the stop band.  These are double-pole filters.  R-C and R-L filters are single pole.  Well into the stop band, a single pole filter attenuates by the frequency ratio to the rolloff point.  In log space, that's 20 dB per decade.  A two pole filter is like two poles applied in series.  They attenuate by the square of the frequency ratio to the rolloff point, which is 40 dB per decase in log space.

For low power (a few watts to 10s of watts) dimmers, the main reason to filter is to reduce the high frequencies so as not to interfere with radio communications.  These are many multiples of the 50 or 60 Hz fundamental frequency.  A L-C filter will attenuate the higher frequency harmonics relatively more than the lower frequency ones.  This is useful since it's the higher frequency content that the regulators care about more.