High white counts always make me think of leukemia (maybe I just always think of the worst possible scenario). But there are a ton of benign things that can make one's white count go up. Fortunately, these benign conditions are much more common than leukemia.
Neutrophils: bacterial infection, inflammation, metabolic disease (e.g., diabetes), stress (even the anxiety of being in the ER can make your neutrophils demarginate; the neutrophil count can double in this setting!)
Lymphocytes: Viral infection (e.g. infectious mononucleosis, hepatitis), immune disease, stress (lymphocytes don't marginate along the inside of blood vessels - so the count doesn't go up as dramatically as the neutrophil count can)
Eosinophils: skin diseases, drug reaction, parasite infection, asthma
Basophils: chronic myeloid leukemia. Okay, this is not a benign thing. But if you see a basophilia, this is the first thing that should come to mind. There are very few, if any, other causes of basophilia.
Monocytes: infection, solid tumors (rarely, the monocyte count goes up when a patient has a solid tumor somewhere), autoimmune disease