Final Fantasy X AeonsValefor

This is the first Aeon you receive. Valefor is a great, winged aeon that has all-round good stats, particularly with speed and evasion. His special attack deals some damage, and causes dely.
Overdrive Valefor's overdrive is Energy Ray. This attack deals a good amount of damage, plus it hits all enemies. If you go back to Besaid village after defeating Dark Valefor, you can talk to a girl in a hut who will give you a strange item. This item will automatically teach Valefor a new overdrive, Energy Blast, which is a more powerfull version of Energy Ray.
In order to break Valefor's damage limit and exceed 9,999 damage, you will need to get Yuna's celestial weapon, the Nirvana staff. Then, Valefor's attacks will exceed the damage limit.

Ifrit
The second Aeon you get in the game. Ifrit is a fire-based Aeon who has great physical power. His special attack, meteor strike, is a powerfull fire attack.
Overdrive Ifrit's overdrive is Hellfire. Basically, this overdrive deals a great amount of fire-based damage to all enemies.
In order to break Ifrit's damage limit, you will need to obtain Wakka's Celestial weapon, the World Champion.

Ixion
The third Aeon you get in the game. His strength and magic are low, but he posesses great defensive skills.
Overdrive Ixion's overdrive is Thor's Hammer. This is giant lightning bolt that deals lightning damage to all enemies on screen.
In order to break Ixion's damage limit, you will need to get Kimahri's Spirit Lance.

Shiva
Shiva is an ice-based Aeon in the form of a beutiful woman. She has decent stats all around, but her agility is exceptional.
Overdrive Shiva's overdrive is Diamond Dust. This chilling attack deals heavy ice damage agianst all enemies..
In order to break Ixion's damage limit, you will need to get Lulu's Onion Knight.

Bahamut
Bahamut is a huge, dragon shaped Aeon. Not very fast, but he is extremely powerful.
Overdrive Bahamut's overdrive is Mega Flare. This is one of the more useful overdrives in the game, because it deals non-elemental damage to all enemies.
From the moment you get Bahamut, his damage limit is broken already and he can already exceed 9,999 damage.

Yojimbo
Yojimbo is the most interesting Aeon in my opinion. He is a warrior who will only attack if you pay him Gil.
Yojimbo has no overdrvies, but posesses four special attacks. The more you pay him, and the better you treat him, the more chance he will perform a more powerfull attack. The most powerfull of these attacks is Zanmato, which kills all enemies straight off, in one hit. This includes ANY of the bosses too, even sin, although you will need to pay Yojimno a LOT of money for the bosses - and even if you do, chances of Zanmato are low.
In order to break Yojimbo's damage limit, you'll need to get Auron's Masamune.

Anima
Anima is an incredibly powerfull aeon with great stats all-round. Her special attack, Pain, causes a lot of damage, and can inflict death.
Overdrive Anima's overdrive is Oblivion. This is the most powerfull overdrive in the game and can deal more then 1,000,000 damage against normal enemies.
From the moment you get Anima, her damage limit is broken already and she can already exceed 9,999 damage.

Magus Sisters
The Magus Sisters are three sisters who each have thier own special abilities. They look like insects (as if they are wearing insect costumes, but more realistic). The downer about these Aeons are that you cannot command them directly - you can give them orders like "Fight!", or "Heal!" - but there is no garuntee they will listen to you, and they may just do what they want despite what you say.
Overdrive The Sister's overdrive is Delta attack. This can only be accomplished when all three of the sister's overdrive bars are full. The Sisters combine thier powers to deal a huge amount of damage with this attack.
From the moment you get the Magus Sisters, thier damage limits are broken already and they can already exceed 9,999 damage.