Through out the series, Jake has exposed a number of many different powers and abilites. This list is going to explain them all.
Transformation
Jake is able to transform from his human form to his dragon counterpart. When in transformation, a blue aroma surrounds him. Jake is also capable of using his powers outside of his draon form and turn a body part to its dragon form.
Fire
Jake is able to harness and munipulate the element of fire. He can breathe it and form his fire to many different shape and sizes. He is also capable of using his fire to make statues evidenced when he breathed fire on a snowman to make an exact replica of his crush Rose.
Dragon Strength
As a dragon, Jake has enhanced strength. At this rate, he is able to withold and take on a very larger and powerful creature. In numreous episodes, he is seen lifting up heavy creatures and objects as well as tare through metal. My personal opinion from watching the show is that he can lift 1-2 tons.
Eye/Ear of the Dragon
Jake is able to see and hear from far distances. He is able to hear through sound blockage and through solid material.
Tail
Jake has a very strong tail that can lift heavy objects. He also uses it to sneak up on enemies.
Flight
Jake can fly at a rate of 178 mph and is quite manuverable. He uses this in combat and to avoid attacks.
Claws
Jake's claws are capable of taring though hard forms of matter. They are also sensitive enough to pick locks.
Durability, Stamina, Agility & Endurance
Jake posesses many acrobatic abilites. He is capable of surving long falls and can withstand his own in a fight as well as take hard blows and hits. Jake is also capable of using his lightning fast speed in battle. He also exposes great endurance and agility as he can fight for extended amounts of time and manuver though small and narrow objects.
Hand to hand Combat
Thoughout the series, Jake has exposes an ability of martial arts. He often uses this in combat agianst enemies. It is hinted the style of martial arts he uses is Kung fu.