Primary cilia: what cell types have non-motile cilia that migrate?
It's hypothesized that planar cell polarity is many cases functionally associated with asymmetry of (primary) cilia (Axelrod (2008)). So, the phenomenon of primary cilium migration could be not that infrequent. One example is the development of ependymal cells in brain ventricules: They are multiciliated and the cilia are motile, but ciliogenesis starts from a single cilium, which is not motile and which migrates from the apex to the rostral end of the cell:


Mirzadeh et al (2010)
Bayly &amp; Axelrod (2011)


Seemingly less clear (for me, at least) cases are non-motile single cilia on the lens fiber cells and may be, embryal node cilia (which are motile in the mature state):


Wallingford (2010) 
Sugiyama et al (2010)