How many Dragons are there in total in Fairy Tail?
According to the Fairy Tail wiki, there are 18 Dragons who have been given a name. 


   However in the Grand Magic Games arc we learn that 400 years ago the world was ruled by dragons. Many a Dragon were slain, and thus, the humans became known as Dragon Slayers.


Dragons with titles:


Igneel - The Fire Dragon King
Metalicana - The Iron Dragon
Grandeeney - The Sky Dragon
Acnologia - The Black Dragon (The Black Dragon of the Apocalypse)
Weisslogia - The White Dragon
Skiadrum - The Shadow Dragon
Zirconis - The Jade Dragon
Atlas Flame - The Fire Dragon
Belserion - The Sage Dragon
Irene Belserion - Queen of Dragons
Elefseria - The Law Dragon
Mercuphobia - The Water God Dragon


Other named Dragons:


Motherglare
Scissor Runner
Levia
Dark Dragon
Rock Dragon
Animus