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: 
Sleeves are good for games that have you shuffle a *lot*. Roborally, for example, shuffles a single deck of cards many times every game, and my cards were significantly worn after a year or two of playing occasionally. Similarly, if the cards just don't seem to be very durable, sleeves might be a good idea.

They're usually mostly pointless for games that don't shuffle much (once per game). The cards shouldn't wear that fast, so unless you prefer shuffling with sleeves or are very protective, there's not really much need.

And sleeves are counterproductive for extremely large decks of cards (think Arkham Horror with expansions) where the stack of sleeved cards would be way too high to be stable.
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.