A long time ago there were only three kinds - red, white, and rose platelets. Advances in cell sorters and more recently in genetic techniques and differentiation studies have led to the identification of a wide variety and complex lineage of cells that comprise human blood.
Roughly at least, how many types of cells are currently identified?
I understand that "types" is a non-technical term, and I'll try to better define what I mean. For example, I do not mean to enumerate each antigen specificity separately because that would make the number fairly large and probably dependent on the individual's history.
One possible definition of a "type" would be that it has been given a name.
I don't mean to include cells that are present due to injury, clean-up, trash collection, or foreign cells including bacteria, viruses, parasites etc.
Just for an example, here is an overview of types of hematopoietic stem cells. There may be further recognized subdivisions, I don't know how far it goes. There are certainly other cells that comprise human blood. (From here.)