What happens when you use Reincarnate ('Destroy a minion, then return it to life with full Health') on a minion that has the Ancestral Spirit deathrattle (Give a minion "Deathrattle: Resummon this minion.)? Does it result in two copies of that minion? Also how does it effect minions like Harvest Golem that summon a minion on death?
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 !
As Shunwoo already explained what happens, I'd like to add a combo: A friend told me about a certain Raptor whose attack becomes double of the attack of an arbitrarily selectable minion on your side. The typical strategy is to have two exemplaries of this Raptor on the field, and to keep alternately sending them back to hand and re-summoning them, thus making them buff up each other. But now imagine instead putting Ancestral Spirit on either of them, and then using Reincarnate!
I think the Raptor in question is different from Unearthed Raptor. But in combination with Unearthed Raptor, Ancestral Spirit + Reincarnate can exhibit quite an amount of power too: Imagine you put Ancestral Spirit on an Unearthed Raptor, then summon another one! There you have two Raptors your enemy can kill both, or never! And with Reincarnate, you can increase this number to three, then to four, then to five... If you have means to get Reincarnate back to your hand multiple times (I think there even is a card returning all cards with the same name), then you can build up an insane army of Unearthed Raptors, that won't die as long as at least one Ancestral Spirit minion survives!
And by the way, Rivendare can truly be insane with these. He's so terrible in each of the combos! For example, if in the first combo you resummon the first Raptor twice, thus having 4 times the attack of the remaining Raptor, plus one with double the attack plus the third one, Rivendare gives you ADDITIONALLY one with 8 times, and one with 16 times! Or for the second combo, as long as you have Rivendare on the field, your Unearthed Raptors will even increase in number! And your growth by Reincarnate will triple in SPC (Summons Per Card)! Additionally, you can put the originating Ancestral Spirit on him - his bulk is really not bad, especially if you get Divine Spirit on him too.