Answer:
No, not all cells have a nucleus. A nucleus is only present in cells that need to divide and multiply, as it contains the DNA.
An example of a cell without a nucleus is a red blood cell, the numbers of these are controlled by the bone marrow and the spleen.
However you forget that we can also have prokaryote cells (bacteria), and they have circular DNA but do not have a nucleus. I think your question was supposed to be "Do all eukaryotic cells have a nucleus", in which case the answer is no.