I was a Peace Corps Volunteer in Ethiopia and surprise adopted my pup from the capitol. By surprise adopt, I meant I found him wandering the streets following strangers around, near the nest he made for himself. I watched him for a few days before deciding to take him back to my tiny village. I know he's 25% basenji because I did a doggy DNA test and he looks like a taller basenji.
He was abused as a puppy and was pretty scared of new situations and people. It took a long time to build his trust and get him comfortable with his new home. But in his natural environment, he was as happy as could be. Our morning routine consisted of me letting him out to wander the village and then return when he was hungry or bored. He would also follow me to the school where I taught or would tag along to whatever errands I had to do for the day. He was pretty well behaved besides some food aggression (only when he had a bone).
I would definitely say that basenjis are very well behaved when they are allowed to sort of do as they please and expend all their energy. Mvdperez did a good job with summarizing some of their behaviors. They are a little stubborn if they don't get their way but they're great dogs!