Solid State Relays (SSR) do work great. Internally they use an LED to close the switch rather than the mechanical coil mechanism used in the classic click relays; these are totally silent.

I am using one to turn on/off the mains power of a 12VDC transformer. The nice thing about an SSR with an input range of 3–30V (a common type) is that you can drive it directly (and safely!) from a Raspberry Pi GPIO pin (3.3V).

Thanks! Will definitely look into them :)