Players choose Diablo 3 Act III for farming for it is easy to stash five Nphalem Valor and easy to find Elites. As the mob density is a little rare after the nerfed, it may not be the priority for power leveling farming. But it is definitely the Number one place to farm Demonic Essence, Diablo 3 Gold and Items.
Choose Act III = =>Heart of Sin = => The Second Heart
Route 1: Clear Tower of the Cursed backwards until your get Arreat Crater level 1. You can continue until you get Rakkis Crossing.
Route 2: Begin with Keep Depth Level 3. There would a pack of Elites not far from the way point. Another pack at the Exclamatory Mark points. The Keep Depths level 2 is my favorite spot. In my personal view, this map is the most dense part of whole Act 3. Of course, the Fallen Maniac adds the challenge as well. Farming until you get Level 1 point.
Route 3: Stone Fort backwards then forward. This route I would recommend to those who would like to get power leveling as well key warden farming.
I do think that actually you can finish the whole Act III if you are bored in certain part. Of course, you can combine the three and create your own farming route. I personally like to start from the town and get to the keep level 1 until level 3. Then start the key wardens. I would like to share with you another popular route by other players as below.