If you're talking about elements, the ones I know of are air/wind, earth, fire, water, ice, nature, lightning, and darkness.
But if you're talking about actual types, then there are a lot. I know some of tu might remember a few of these types from Harry Potter o so, but there were Peruvian Vipertooth, Chinese Fireball, Swedish Shortsnout, Welsh Green, Hungarian Horntail, Night Fury (I put this for tu fellow HTTYD fans), and a few others I can't remember the names of.
there are the elements : fire, water, wind/air, earth, spirit, light, dark, then there are the flying dragons, water dragones and th the lung dragons/Chinese dragons