Study after study has shown the border collie to be the easiest to train. From my experience as a professional trainer and after training well over a thousand dogs I would agree, the BC is the easiest to train.
BUT the BC is a handful of a dog. It needs a JOB. You can't get one and put it in the backyard or it will create it's own interesting fun. You won't like what it chooses!!! BCs need specific type of owners who are extremely active and have loads of time to put into training. A BC needs to do something like herding, agility, flyball, disc dog, etc. Of course, I know couch potato BCs, too, but generally speaking a well bred BC from good lines will need to be working.
However, that also doesn't mean that other breeds aren't intelligent. One of the problems with measuring "intelligence," in either dogs or people, is that we really can't avoid measuring what the dog knows or has learned or can learn.
So breeds that were bred to work with humans - in other words bred specifically for the trait of being eager to learn from a human - will do better at intelligence tests. They are more eager learners - but does this make them smarter?
Afgan Hounds are generally considered to be among the dumber breeds. However they are sight hounds. They were bred to work completely independent of the hunter, working a mile away and holding at bay the prey until the hunter appeared to kill it. They were not bred, like say a herding dog, to follow extremely closely the commands of a human.
So a sight hound really doesn't care much what the human thinks, asks, does, etc. during training. But does that make them dumg? No...it makes them sight hounds.