Pilosocereus aurilanatus
I water this during it's growing season, with just the occasional splash in winter. Of course, it likes full sun and looks kind of ugly otherwise.
It almost never branches unless you cut the top off. The cut top roots easily. This plant pollinates itself and makes lots of viable seed. Our local ant population can eat the whole apple-sized fruit within about two days. If the local squirrels don't get it first.