WARNING: The following contains spoilers for the Attack on Titan manga and anime.
Attack on Titan's Nine Shifter Titans are the most powerful entities in the entire world of this post-apocalyptic fantasy series. Descending from the original Titan, Ymir Fritz, the Nine Titans are roles that are passed down from generation to generation, each with their own unique abilities. Naturally, with a set of powers like these, these Titans have legendary status.
When Ymir Fritz died, her abilities passed through into the Fritz family line, which later extended to the Reiss family and others of noble birth. While Titans can be found across the world, the powers of the Nine outrank the rest. Some, once the host has been devoured and their Titan power assimilated, can even carry multiple powers at once, and one individual in Attack on Titan (Eren Jeager) amasses a greater deal of proportion than most. However, all those who inherit one of the Nine Titans' powers also inherit the Curse of Ymir: a shortened life sentence. After all, the brightest flames always burn fastest.
Regardless, the Nine Titans remain the strongest around, though their numbers have recently been whittled down to a few select individuals.
The Founding Titan Is the Original and Greatest Titan
When Ymir Fritz became the first Founding Titan, she gained the ability to control other Titans. From Ymir's bloodline, all other Titans emerged, giving an entire race of people the latent ability to become monsters. The original plan set forth by Eren's father, Grisha Yaeger, was to become the Founding Titan in order to dominate the will of all other Titans for his own purposes. However, when Eren ultimately devoured his old man, he gained the powers of the Founding Titan...
... Or, so it seemed. The powers of the Founding Titan are actually passed down via royal blood, so anyone who inherits the powers without royal blood can't actually access its full abilities. After encountering his half-brother, Zeke, Eren developed the ability to, on occasion, control other Titans, including the Titans inside the walls around Paradis Island. In addition, due to these powers, he can recover from lethal attacks, such as having his head blown off.
The Founding Titan is not immortal, though. It's actually powered by the "Source of All Living Matter," the core entity that gives the Founding Titan its powers. Destroying this destroys the entire Titan race.
The Attack Titan Has Memories of Past and Future Events
The Attack Titan is one of the most vicious and violent Titans around. On top of the strength and might of an already powerful Titan, this entity can also receive and interpret memories of its past incarnations, as well as memories of future events. These memories direct the actions of the Attack Titan, pushing it to fight for freedom and justice -- forever moving forward.
The prior owner of the Attack Titan's abilities was Eren Kruger, who, knowing the future incarnation of the Attack Titan (Eren Jeager), deliberately passed down his abilities to Grisha Yaeger, Eren's father, well aware that this might one day bring revolution to the world.
The more Eren uses the powers of the Attack Titan, the more control he has over his abilities, being able to pierce through all obstacles with his colossal strength and power.
The Colossal Titan Can Topple Walls With One Kick
One of the first Titans we see in Attack on Titan, this skinless giant has the power to evaporate parts of its body and release great quantities of steam, burning and melting objects around it with its heat. It stands far, far taller than almost all of its compatriots, being one of the biggest Titans around at 60 meters in height.
Bertolt Hoover was the previous owner of this immense power, giving him enough strength to kick down Wall Maria with one strike. However, eventually, Bertolt met his end, and his powers were passed to Armin Arlert, whose Colossal Titan form (also known as the Colossus Titan) while massive, is also far more gaunt and less physically hot than his predecessor.
Armin ends up fighting Eren as the Founding Titan, allowing Mikasa to sever Eren's head in the process. Following Eren's death, Armin lost the power of the Colossal Titan. It's uncertain if this spared him from the Curse of Ymir's negative effects, but he remains a major figure in Attack on Titan's society, deemed the "Man Who Killed Eren Jaeger."
The Female Titan Is the Only Feminine Member Of the Nine
The only distinctly female Titan among the Nine, the Female Titan remains one of the most powerful around. By screaming, it can draw in Pure Titans to her beck and call -- though it can't control them in the way that the Founding Titan can. It can also harden parts of its body to use as a weapon.
The current Female Titan is Annie Leonhart, a refined combatant who uses her skills with martial arts and crystalline body to make it into the ultimate weapon. She is the first of the other Nine Titans Eren faces off against, and the two barely survive their encounter. Annie's body ultimately becomes unstable, her skin becoming hardened to the point where her body is totally paralyzed.
She is only freed when Eren uses his power as the Founding Titan to undo all Titan hardening, awakening to fend off the Jaegerists on Paradis Island. Despite having only a few years left to live leading up to the Curse's end, Annie actually survives the events of Attack on Titan.
The Armored Titan Is Attack on Titan's Toughest Fighter
Taking the Female Titan's ability to form crystalline armor, the Armored Titan takes this to a whole new level. It's able to develop a suit of armor all over its body, turning itself into a Titan left completely impenetrable, except for vital points of articulation necessary for movement.
The current wielder of the Armored Titan ability is Reiner Braun, who first helped bring down the walls surrounding Paradis with a running start, charging at it like a football lineman. Reiner also helps stop Eren from reforming after his head is removed, going on to help end the Titan's Curse alongside Armin, Mikasa and the others.
The Beast Titan Can Control Other Titans With Its Shout
The monstrous Beast Titan possesses animal-like strength and a similarly animalistic appearance. It's most notable for being able to throw any item within reach practically as far as it wishes -- and with disturbing accuracy. At 17 meters in height, many regard the Beast Titan among the strongest Titans around. But its most devastating ability is non-physical: By having other Eldians consume his spinal fluid, Zeke can then use the Beast Titan's shout to awaken them as Pure Titans when he chooses and control them.
Able to overpower even the Armored Titan with ease, thanks to its beastly power, the Beast Titan powers used to reside within Zeke Yaeger, the half-brother of Eren. This adversary long-manipulated both humanity and Titans on behalf of its masters, until Zeke is ultimately slain by Levi Ackerman in the final battle.
The Jaw Titan Has a Deadly Bite
As one of the smallest and swiftest of the Nine Titans, the Jat Titan's abilities allow it to crush and shred any and all things between its teeth and claws.
Originally, this power belonged to Marcell Galliard, but following his demise, the powers are passed down to Ymir (not Fritz) and then to Falco Grice. For a long time, Falco struggled with the powers of the Jaw Titan, often losing control and becoming ballistic. It's only in the final chapters of Attack on Titan that we learn the Jaw Titan can sprout wings and fly.
The Cart Titan Is the Ultimate Defensive Unit
Another remarkably small Titan, this four-legged "giant" stands at only four meters. It's known for its bizarrely canine appearance and ability to remain transformed for long stretches of time -- two months at a time being its record before its is forced to return to normal.
While masculine in appearance, the current Cart Titan is Pieck Finger, a sweet woman who, due to her long stretches in Titan form, has found that walking on all fours is actually more comfortable for her than not. She ultimately ends up joining her fellow Warriors to help stop Eren's Founding Titan at the end of Attack on Titan, moving on to live her full life after the events of the series.
The War Hammer Titan Can Create Weapons
The last of the Nine Titans to be revealed in Attack on Titan is the War Hammer Titan -- a Titan able to create weapons from its calcified flesh. This includes swords, clubs, and, yes, war hammers. Rather than its host transforming into the Titan, the War Hammer Titan can be created and controlled from a distance by a "flesh cord," creating a Titan body while the real intelligence sits comfortably far away.
Originally controlled by the younger sister of Willy Tybur, Eren finds and devours her during the Marley raid, obtaining the powers of the War Hammer Titan. Adding this to his Attack and Founding Titan, this Shifter in his arsenal made Eren even more unique. Eren utilizes this power to fend off multiple Titans during the final battle, establishing himself as one of the mightiest -- and controversial -- figures in the world of Attack on Titan.