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 wewe might remember a few of these types from Harry Potter au so, but there were Peruvian Vipertooth, Chinese Fireball, Swedish Shortsnout, Welsh Green, Hungarian Horntail, Night Fury (I put this for wewe 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 dragoni and th the lung dragons/Chinese dragons