Some common causes of low platelets during pregnancy include gestational thrombocytopenia, pre-eclampsia, HELLP (hemolysis,elevated liver enzymes, low platelets) syndrome, immune thrombocytopenic purpura (ITP).
Less common causes include systemic lupus erythematosus, lupus anticoagulant, human immunodeficiency virus (HIV) infection , B12 or folate deficiency, hyperthyroidism, massive transfusion, prosthetic heart valves, thrombotic thrombocytopenic purpura (TTP), sepsis , disseminated intravascular coagulation (DIC) , hypersplenism, hemolytic uremic syndrome, hereditary thrombocytopenias (Bernard Soulier ,May-Hegglin, Wiskott-Aldrich, Upshaw-Schulman , thrombocytopenia with absent radius), alcoholism, leukemia, aplastic anemia, and drugs (heparin,  zidovudine, sulfonamides, trimethoprim-sulfamethoxazole,  sulfonamides, valproic acid, phenytoin , digitalis, ranitidine, cimetidine, ampicillin, penicillin, alpha-methyl dopa, ethanol, aspirin,acetaminophen, indocin)

Some causes of an increased platelet count include myeloproliferative disease ( essential thrombocytosis, chronic myelogenous leukemia, polycythemia vera, myelofibrosis ) and reactive thrombocytosis (postpartum ,hemorrhage, iron deficiency, inflammation, decreased or absent spleen function)  

References:

1. Abbassi-Ghanavati M, Greer LG, Cunningham FG. Pregnancy and laboratory studies: a reference table for clinicians. Obstet Gynecol. 2009 Dec;114(6):1326-31. PMID:19935037
2. Eby CS. Hematology and Hemostasis During Pregnancy. In: Gronowski AM ed. Handbook of Clinical Laboratory Testing During Pregnancy .  Totowa , NJ: Humana Press , 2004:202-204.
3. Moss RA. Drug-induced immune thrombocytopenia.1980;9(4):439-46. PMID:645205