My understanding is that there are two broad categories of cilia: motile and non-motile (also called primary.
Examples of the former include sperm flagella and the cilia of epithelial cells that line the airways.
Examples of the latter are mostly single cilia that protrude from the cell and act as an antenna, usually packed with certain receptors (HH pathway, Notch pathway etc.)
In the inner ear, a primary cilium called the kinocilium extends out of the center of the apical side of hair cells and migrates to the lateral side over the course of a few days. This cilium is non-motile, it is simply anchored to a basal body which is pulled to one side of the cell.
Does anyone know of another such example in any other tissue? A single non-motile primary cilium whose basal body migrates along the apical plane of the cell after docking with the cell cortex.