The oldest system I have would be the NES. My brother received it sometime before I was born. I'm just holding onto it for him, though - it doesn't get played right now. I actually intend to clean it all up and retrobright it before sending it back to him... eventually...
The oldest system I have that still gets occasional use would be my Gameboy Color, which I received, with Pokemon Red, for Christmas when I was 8 or 9. Unfortunately, I need to find a better plastic polish, to take some light scratches out of the lens, and until I do, it will remain disassembled... I've also been contemplating using the board for a complete boxypixel overhaul, but there's something about still having my full original GBC that I'm having a problem getting over...