Here are icons of Dragon-Type Pokemon that are available in the game through trade or evolution by Level in Y (Dragalage isn't available in X).
Now, you don't want to get your Dragon too early. Here are all the Dragons that you can catch their pre-evolution before the 5th Gym Badge.
I just cut the list in half. Now, you want to be able to actually use this dragon in the game, right? Dragons normally take a long time to train, some evolving at almost Level 60. Here are Dragons that evolve pre-level 50 into their final forms.
You want your Dragon to be strong, right? Here are dragons with a BST of 535 or higher.
(540) (600) (540)
Kingdra
Kingdra can do anything. It has 95 in every stat besides Speed and HP (85 and 75 respectively) and has a wide movepool that encompasses both physical and special moves. Being a water type removes its Ice weakness, leaving its only weaknesses to be Dragon and Fairy, and it covers both quite nicely. It has access to Sniper, and plenty of obscure moves like Octazooka learnt by Seadra. Horsea/Seadra is found at Ambrette Town and Route 8 by fishing and evolves into Kingdra by trading with a Dragon Scale (5% chance Horsea/Seadra holds it in wild).
Item: Mystic Water
Nature: Modest (^SpAtk vAtk)
Ability: Swift Swim
EVs: 252 SpAtk, 252 Spd, 4 HP
Octazooka
Flash Cannon
Double Team/Scald
Dragon Pulse
Garchomp
Everyone knows Garchomp. The unstoppable Dragon-Ground type that got banned in OU with Sand Rush. In X & Y, it just got a lot scarier with a Mega Evolution (upping its amazing BST to 700) with Sand Force and in a sandstorm, this beast is unstoppable. 170 Attack is nothing to mess with at all. Gible is found at Route 13 and evolves to Garchomp at level 48.
Item: Garchompite
Nature: Adamant (^Atk vSpAtk)
Ability: Rough Skin
EVs: 252 Atk, 252 Spd, 4 HP
Earthquake
Dragon Rush
Stone Edge
Poison Jab
Haxorus
This beast rivals Garchomp with 147 Attack, a diverse movepool and great stats overall. Even though Mold Breaker is its only useful ability, it has coverage against all of its weaknesses and Axew, its pre-evolution, is found very early in the game at Connecting Cave. Evolves into Haxorus at Level 48.
Item: Scope Lens
Nature: Adamant (^Atk vSpAtk)
Ability: Mold Breaker
EVs: 252 Atk, 252 Spd, 4 HP
Earthquake
Dragon Claw
Poison Jab/Iron Tail
Dragon Dance
