Reincarnate a minion with the Ancestral Spirit deathrattle

Let's take the example you presented with the Harvest Golem.

If you play Ancestral Spirit on him, and then use Reincarnate, he will die, spawning the 2/1 token, then he will respawn twice, once from Ancestral Spirit and once from Reincarnate. So at then end you'll have, one 2/1 token, and two 2/3 Harvest Golem.

Now just for fun, think about the following combo : play Baron Rivendare then next turn play Leroy, use Ancestral Spirit twice and Reincarnate !!! Enjoy !