Question: Card sleeves are probably be a no-brainer for board game collectors who want to keep their games in pristine condition for as long as possible, or for CCGs where an individual card may be very difficulty to replace. 

For non-collectors playing games like Agricola, 7 Wonders, Mage Knight, Pandemic, etc, when does it make sense to use card sleeves and when doesn't it make sense?

Answer: 
As card sleeves are quite cheap, it's just a matter of personal preference. Some people like sleeves (I do) others don't (some of my friends).

One case I could argue for sleeves is when you have a card game and plan on maybe buying an expansion later. The cards from the base set would be rugged from use, while the expansion would be pristine and shiny. It will be visible. In case of sleeves, you just put all the cards into new sleeves and voila, every card looks the same.
Another, not obvious reason when you want to sleeve your cards, is when you suspect your cards could be easily damaged.

It can happen, when you are going to play some multiplayer games like Dixit Odyssey on your lake holiday with a bit drunk friends, when everyone probably would have their hands dirty, not to mention a few times sleeves saved my cards when someone fall over candles, or some glasses with juice or coke. Then, you are really happy that you bought sleeves.