can you play any Mario kart games on original wii system.  How do I know which games will play on original wii.?

Yes. There was a Mario Kart game for the Wii. Mario Kart Wii.

You could also gain access to older versions through the Virtual Console, though the Wii also can play GameCube games, so you could get the physical copy of the GameCube Mario Kart game & play that as well.

Right now, the only Mario kart titles you can play on the ORIGINAL Wii (RVL-001) are...

* Mario Kart Wii

* Mario Kart: Double-Dash (GCN; Requires Gamecube controller)

Games that WERE available on the Wii via the Wii Shop channel BEFORE it was fully shut down are (you can still download them if you purchased them prior to the shutdown, as the Wii Shop is in archive mode)...

* Super Mario Kart (SNES VC)

* Mario Kart 64 (N64 VC)

Please be aware that BOTH Virtual Console titles will require you to have a Gamecube controller OR a Classic Console / Pro controller as you need the extra buttons & will refuse to start without one.

With virtual console shut down, there is no longer any way to get older versions of the game to play on your Wii.

The only Mario Kart game that is playable on the Wii is Mario Kart Wii, which will no longer have network support.  You can only play single-player or local-multi-player.

pay attention on the games systems and look up and read the owner's manual