Im sure VEEPS and AvgasDynasour are in a better position to answer your question more precisly. But from the back of my mind, there is one An-22 flying for Antonov Airlines, UR-09307. This one flew from LUX to AMS the day before yesterday.
The Russian AF, not sure which regiment, also flies 2 or 3 An-22s on a more or less regular basis. Even one in a great camo livery!