To evaluate the safety of zalcitabine (dideoxycytidine; ddC) alone and in combination with zidovudine (AZT) versus AZT alone when administered to asymptomatic patients with a CD4 count = or < 200 cells/mm3 and symptomatic patients with a CD4 count = or < 300 cells/mm3. To compare the effectiveness of ddC alone and in combination with AZT versus AZT alone.