So, I started playing a blue-black mill/control deck and I have a question a friend and I recently ran into: if I take control of a player for their turn (say with a card like the new Emrakul) and I exile their commander, can I chose to put their commander in exile? Also will it stay there? Is that still the players choice? Is this also applicable to hand, deck and graveyard? Thanks!

From the comprehensive rules:

The decision to put one's commander into the command zone instead of exile (or graveyard, hand, library) is made by the controlling player.

Therefore, it's possible to exile a commander by controlling its owner and choosing not to apply the replacement.
This will effectively leave the card in exile until the game ends or another effect (such as Pull from Eternity) allows to move it elsewhere.

The interesting thing here is that the Commander rules say owner:
"If a Commander would be put into a library, hand, graveyard or exile from anywhere, its owner may choose to move it to the command zone instead."

If you control a player you don't suddenly become the owner of their cards. This phrasing may have been chosen to prevent the feel bad situation when you completely lose access to your general as s/he gets exiled.

The owner doesn't change, the one who makes the choice does.

This. If you control the owner, you make the choices the owner would make. If I control you general and someone else casts Final Judgment, I don't get to choose where your general goes because I'm not the owner. If I slaver you and someone else uses Swords to Plowshares on your general while I'm controlling you, I do get to make that choice.

That said, F$#% Mindslaver, Emrakul, and anything else that does this. I hate all of those cards.

I agree, I think that is what the rule is saying (the controlling player makes those choices). That said, I think the rule would be better if it didn't say that, and that the decision where to place your Commander would be put into the same category of "choices" as whether you concede or not, which is a choice that the controlling player does not get to make.