Note: Like any other game he's in, Akuma's overpowered moves are balanced out by a low defense. He takes more damage per hit than most characters.
Zugai Hasatsu: F+HP
Akuma does a downward chop. Basically it's just like Ryu's collarbone breaker. Overhead.
Senpuu Kyaku: F+HK
Just like Ryu's. It's a single rotation of the Hurricane Kick.
Tenma Kuujin Kyaku: D+HK
This is Akuma's ever famous diving Kick. Good for surprise attacks and has great priority, but watch out for Dragon Punches.
Gou Hadouken: QCF+P
With a grunt, Akuma throws a typical Hadouken. Knocks down if done in close, though.
Skakunetsu Hadouken: HCB+P
Akuma tenses up for a second before throwing a bigger, flaming, three hit Hadouken. Easy to see comming.
Zankuu Hadouken: QCF+P in the air.
Akuma throws a Hadouken at a downward angle with one hand.
Gou Shoryuken: DP+P
Akuma's Dragon Punch has more forward range than Ryu's, but less than Ken's. It's multi hitting.
Tatsumaki Zankuukyaku: QCB+K
Well, Ryu got THE Shotokan fireball, and Ken got THE Shotokan Dragon Punch, so Akuma got THE Shotokan Hurricane kick. It's basically a combination of Ryu's and Ken's, since in knocks down and hits multiple times.
Ashura Senkuu: DP or RDP+2P or 2K
Akuma's teleport. Akuma slides forward on one foot with shadows behind him. He's completely invulnerable during the move, but he is open for a split second as he "phazes" back in.
Akuma flips forward through the air. You can go into several moves from here.
Hyakki: Do nothing during a Hyakkishu.
Akuma does a sliding kick upon landing.
Gou Sho: P during a Hyakkishu.
Akuma does a palm blow to his opponent's face. This move knocks down.
Gou Sen: K during a Hyakkisu.
Akuma drops back first on his opponent.
Hyakki Gou Sai: P when close during a Hyakkishu.
Akuma slams his opponent into the ground.
Kyakki Gou Tsui: K when close during a Hyakkishu.
Another throw, this is the most powerful one.
Messatsu Gou Shoryu: QCF(x2)+P
Akuma mimics Ken and does a Shoryu Reppa. Doesn't have quite the damage potential as Ken's, but is otherwise just as good.
Messatsu Gou Hadou: HCB(x2)+P
This is just like Ryu's Shinkuu Hadouken, but not quite as damaging. The tricky motion makes it somewhat useless in a heated fight.
Tenma Gou Zanku: QCF(x2)+P (air only)
Akuma throws a souped up version of his air fireball. This move pushes Akuma up into the air, and gives him a descent similar to a Dragon Punch.
Messatsu Gou Rasen: QCB(x2)+K
Akuma rises into the air with a Hurricane Kick. Basically a Shinryuken, but has slightly more forward range.
Shun Goku Satsu: LP, LP, F, LK, HP (Max level ONLY)
Akuma slides forward in a similar stance to his teleport, and if he touches his opponent, the screen goes white as Akuma beats the crap out of his opponent. When the light fades, the opponent is on the ground and Akuma has his back to the player with a Japanese symbol glowing on his back. The move is unblockable but easy to avoid.
Kongou Kokuretsu Zan: D, D, D+2P (Max level ONLY)
Akuma raises his fist above his head, then slams the ground HARD, surrounding himself in "Evil Intent" flames. Very damaging, but not as much as the Shun Goku Satsu. Easier to perform and to hit with, though.
Power-Up Mode: Shin Akuma
Effect: Akuma turns into Shin Akuma, with golden colored hair, and a purple gi. He gains speed, power, and the ability to throw two air fireballs at once, like Akuma in SSF2T.
Downfall: Akuma gains an even bigger damage handicap than usual.