Practically all emission and noise control equipment is mandated. Generally it isn't mandated "thou shalt have a catalytic converter", but what's mandated are the emission limits of CO, HC, NOx, evaporative emissions when the engine is not running, etc., and these limits in turn largely dictate the course of action for the manufacturer. The manufacturer declares the emission control equipment used on the vehicle (it's on a sticker somewhere on the vehicle) and that's what must be on the vehicle for it to be in compliance with emission regulations.
For automotive applications, OBD-II (on-board diagnostics) has been mandated since 1996.
Closed crankcase venting (the crankcase has to be vented into the engine air intake) has been mandated on automotive applications since the late 1960's and were the first emission control device to ever be mandated.
If you are talking about something other than emissions or noise, please specify.