I have seen every episode of every gen of MLP made today as well as read every comic and book I have been able to find somewhere. I said this so you will understand that this list I am making of every kind of dragon that has been in MLP is extremely accurate.

Wyrms: Lets get these guys out of the way first since they are the ones most people know as dragons. A wyrm for those that don't know are classical western dragons.

Stratodons: This is our MLP original dragon specie and they come from the first MLP episode ever, the G1 pilot episode Rescue At Midnight Castle. With that said these guys are nothing more but wyrms.

Drakes: Drakes are western dragons without wings and they were in G1, however this may cause confusion as G4 has use the term to mean a male dragon.

Wyvern: Western dragons who wings and forelegs are one. We have seen these guys in the G4 comics.

Lindwurms: Serpent like dragons with forearms, we saw one of these guys in the first episode of G4. Of course I have to add that as of right now we don't know if lindwurms counts as dragons in G4.

Wurms: Serpent dragons, this one is a little odd for we only saw one dragon like this in the G1 comics but he didn't start of as this kind of dragon but was draw this way after appearance.

Sea Wyrms Wyrms who wings are really giant fins, this was what that wurm I was telling you about earlier started out as.

Amphipteres: Serpent dragons with wings, we saw some in the G4 comics.

Storm Dragons In G3 we met a dragon that could control the weather with their breath, creating all kinds of storms.

Royal Pet Dragons: Another MLP original dragon specie this was what Spike was in the G1 toy line and comics. He wasn't the only one, there were six others his age sold as toys plus Spike's Great-Great-Grandfather and Great-Grandfather in the comics as well as three others from the comics. Royal pet dragons were called that because the ones who got toys were the pets of pony royals. These dragons could cast spells and breath fire.

Yung/Ryu: Hinted at in G4 yungs are eastern dragons with four toes while ryu are eastern dragons with three toes. I put both names down for these guys because MLP dragons have four fingers yet three toes so they could use either name for them.

Draconids: This comes from pop culture as a name for humanoid dragons, We seen them in G1 and in G4 as both teenage dragons and adults.

Basilisks: Dragons with eight legs, we seen one and only one in G4 and it was the female dragon of that gen.

Salamanders: Salamanders are dragons that look like newts and well salamanders, we saw one in the G1 comics. Note there was also a non-dragon villain name salamander in the G1 show.

Half-Dragons: The comics have said these were a thing but we haven't seen any let.

Stone-Backs In G1 stone-backs were giant armadillos like creatures and they were never said to be dragons in the show yet Hasbro has listed them as half-dragons in everything they ever done with them. Even the script called them half-dragons.

Dagons: This name comes from pop culture for mermaid like dragons, we saw a group of them in the G1 comics where they were only called sea monsters.

Draconequus: Well the name means half-dragon half-horse so yeah Discord counts here.

Here is a quick list of creatures that may or may not have been MLP dragons. I say this because they both follow the rules MLP seems to follow of what counts as dragon but at the same time it was still unclear if they were or not.

Alligatorsaur: A large dinosaur like alligator creature, the one we saw was chasing a strange little cursed man because the curse on the man destroy the alligatorsaur village.

Muddy Mud Monsters: A group of generic dinosaurs who were cover in mud and took over a land of talking lizards. Some ponies came by and the dinosaurs decided they would turn the ponies into muddy mud monsters. But the lizards found that the ponies had soap and use soap bubbles to kill all the muddy mud monsters and get rid of the mud.

Mo'o: Okay this one will need more explaining then the others. First there was a minor G1 villain on the show that was a shape-shifting lizard man, we never heard of what his race were called nor did we see any other lizard man or learn if this was a power all his kind had or not. However in polytheistic belief or at least Hawaii polytheistic belief there is a shape-shifting lizard dragon tribe called mo'os, and they often take human like form, some even used to be humans before dying and being reborn. Was the lizard man a mo'o? I don't know but they are similar to each other,