What cells don't have a primary cilium?
It seems that, by and large, most animal and plant cells have primary cilia. To quote from this open access paper: 


  ".[..] organisms that form cilia have a basal body or centriole-like structure as their microtubule-organizing center, whereas those that do not [e.g., yeast, higher plants] use morphologically distinct structures for organization of their microtubule cytoskeleton."


Other cases where cells lack primary cilia are when they possess motile cilia (e.g., sperm are mono-ciliated, respiratory epithelia are multi-cilliated).


Fry AM, Leaper MJ, Bayliss R. The primary cilium: Guardian of organ development and homeostasis. Organogenesis. 2014 Jan 1;10(1):62-68. Epub 2014 Apr 17.