Hadoken            
+ P (can be done in air) 
The definitive fireball is Ryu's.  It travels straight on ground and in the air.  This is the best fireball in the game and is a classic.  'Nuff Said.  Ken's fireball travels about 2/3 of the screen and then it dissipates.  Not very useful.  It goes down at a 45 degree angle when thrown from the air.  Akuma's fireball is purple and goes the full length of the screen.   In the air, it travels down at a 45 degree angle as well.  No complaints here.

ShoRyuKen 
+ P  (can be done in the air only with Ken)
A rising uppercut attack.  You are INVINCIBLE during the rising part of this move.  Use it to your advantage.  Excellent anti-air move.  However, use the Jab version most as the other ones leave you too open if you miss or if it is blocked( which happens quite often thanks to air blocking).  The ShoRyuKens of the 3 characters are very much alike.

Hurricane Kick 
+ K (can be done in air)
This is still the same classic one since the beginning.  Ryu's is the one hit knockdown hurricane kick.  In the air, it spins in an arc according to your jump.  Don't forget about this move as it is still very essential and useful.   Ken's hurricane kick hits multiple times and has an arc to it.  Akuma's hurricane kick goes straight like Ryu's but it hits multiple times. 

Shotokan Switch
+ P
This move will change Ryu to Ken or Akuma or even back to Ryu depending on which button you press.  QCB + Jab will change you into Ryu (if you aren't him at the time you do it), QCB + Strong will get you Ken, and QCB + Fierce will get you Akuma (yes!).  Ryu turns his back to the screen and changes colors, depending who he is changing to.  He then  possesses all the moves of the character which he is imitating!  However, this move consumes a level of super bar so don't use it too much.

Moves Exclusive to Akuma

Teleportation
+ PPP/KKK (to go forward)
+ PPP/KKK (to go back)
Akuma will teleport leaving trails of himself behind him.   He is INVINCIBLE during the actual teleportation but in the end can be attacked.   Punch will take you all the way across the screen or back, and Kick will take you halfway across the screen or back.  A very useful move and one that should definitely be used to get out of corners, get on the other side of your opponent and unleash a super, etc.  Just know that after you teleport, you are vulnerable for a second after the teleportation.  You can get a super stuck in your face! 

Diving Kick
+ K (air only)
Akuma will dive down at a 35 degree angle with his foot extended.  Hits multiple times.  Mix up with air fireballs to confuse the opponent.  If your opponent is right next to you, jump back and pull this move off immediately.  You could catch him off guard.

Super Moves 

Ryu's
Shinku Hadoken
+ PP (can be done in air)
Ryu releases a large beam of energy from his hands which goes straight across the screen.  The damage this super does is good, and it is the only beam super which can be done in the air.  Use that to your advantage.   However, it can't be comboed into anymore in the air.  On the ground, try Standing Fierce XX Shinku Hadoken.

Super Hurricane Kick
+ KK
Ryu remains in place while spinning and kicking.  This super has a "vacuum effect" which will suck the other player in if they are close enough.  Try sweeping the other player with Crouching Roundhouse, then OTG into the super hurricane kick.

Shin Shoryuken
+ PP
Ryu hits his opponent 3 times with a powerful version of the Shoryuken.  If he connects in the air, it will hit the opponent 8 times.   Useful only in a few choice situations.  However, try launching the opponent with Crouching Fierce and then execute this super.  It just might be enough damage to kill the opponent.

Ken's
ShoRyuReppa
+ PP
Ken performs multiple ShoRyuKens while moving forward, his fist surrounded with flames.  Good super.  Do Crouching Forward Kick followed by this super. 

Shin Ryu Ken
+ KK
Ken does a powerul straight-up ShoRyuKen all the while surrounded with flames.  Takes off GOOD damage.  Do a Crouching Fierce followed by this. 

Running Hurricane Kick
+ KK
Ken pulls back his leg, and then runs forward kicking with his feet surrounded with fire.  After kicking multiple times, he performs a hurricane kick which then arcs up. He kicks them one last time, sending them smashing into the ground.  Good super, but try to do it from a close distance, as it can be seen coming from a mile away.

Akuma's
Messatsu Gou Hadoken
+ PP
Very similar to Ryu's Shinku Hadoken.  However, Akuma can't do it in the air and it doesn't last as long.  Still, a good super to use if you're in Akuma mode.

Messatsu Gou Shoryuken
+ PP
It is exactly the same as Ken's ShoRyuReppa. 

Tenma Go-Zan Ku
+ PP (air only)
Akuma unleashes several air fireballs from where he is in the air.  Does great block damage.

Shun Goku Satsu (The Raging Demon)
Jab Punch, Jab Punch, , Short Kick, Fierce Punch
One of the best supers in the game.  Howeverm it is a level 3 super.  Akuma glides forward, and if he touches the opponent, the screen turns white as he unleashes a can of whoop ass against him!  Then the screen turns normal again and you see Akuma standing over his opponent with his back to the screen.   It goes a LOT LESS distance than it did in MSHvsSF.  Combo into it, like doing a diving kick first or a jumping RoundHouse. 

Misc Info.