Jake is the first dog I've ever owned so I can't really compare his intelligence to other breads but I've come to be quite impressed with how smart he is. There are two specific areas that come to mind.
1. Pattern recognition.
He is very good at recognizing patterns. If I bring him into the garage with the overhead door closed he knows he's going in the crate and he resists moving forward. If the door is open, he knows we're going into the car and he walks just fine. Another example is that 2-3 blocks before we get to the dog park he starts to realize where we're going and he gets excited. If he sees me put on a jacket he'll go stand by the door.
2. Sound filtering.
It's interesting to see which sounds he'll pay attention to and which ones he ignores. One day I had a friend who was trying to get Jake's attention by clapping, shouting, and generally making a fool of himself. Nothing worked. Alternatively, I barely have to whisper his name and his head shoots up. In general, he's very good at figuring out which sounds are "important".
Are there any other forms of intelligence your basenjis seem to excel at?