The 3rd type of transport here are the "special hires" or "specials." They are the equivalent to the USA taxi. They are usually small cars, sometimes mini vans. You can pick one up on the side of the road or you can get a name of someone who has one and call them to come pick you up and take you where you want to go. They are people who have their own car and use them to make money or the owner hires someone to drive the car for them.
These drivers for the most part are ok. You would have them take you somewhere specific when you didn't want to ride the Matatus or at night to be safe.
The upside to these are they can take you places that the Matatus can't, you are in the car by yourself, you can usually stay clean and you are on your own schedule when you get one. The downside: They AREN'T cheap.
Sorry, no funny stories to tell you about these guys!