First lets not forget that all ultras/supers build off of the original special move set. But there are some characters that have that exception such as Gouken and Akuma. With that being said:

Ryu new ultra should be a combo attack that ends with a hurricane kick. Also bring back his reverse step in kick special from SF3.

Ken could have another combo ultra that ends with a rolling air throw for flashiness.

Guile could use Charlie's combo attack that ends with an insanely fast sonic boom for some good damage knocking the opponent on the other side of the screen.

Akuma should just get his arieal chop thing back. Yeah it would be a super cheese move online but whatever. He was meant to be a super cheese player because he is evil.

Balrog could steal one of Dudley's supers for SF3 and make a joke about it in his victory comment since he is a dirty fighter. Or throw a rose after the combo

Bison could start a scissor kick combo ending in a mind controlled CammyJuli/Juni finisher. During the Cammy/Juli/Juni portions he would teleport out of the combo and hover high above the ground laughing with his arms crossed.

Dan could copy Sagats Tiger Destroyer into his own version and call it the Sagat Destroyer since Sagat killed his dad. He has to scream out "Sagat Destroyer" though when doing the move.

Zangief could start with a left, right combo of banishing fists. The first to the body then the head followed by a running/leaping power bomb.

Cammy & Gouken could have some sort of ariel ultra. Be it starting in the air like Akumas air fireball or as an air counter like Gen's super.

That's all I can think of right off the top of my head. Please capcom do something awesome with the new ultras/supers. Give us a reason to use them other then they may be stronger then the other old one's.

Akuma
can punch the ground and all this energy comes surging up

Cammy
can do a cannon spike and than the opponent hits the ground in front of her and than she does an spiral arrow straight down right on their chest. she is still in the air when the enemy lands.

I'm guessing ryu might get his denjin hadouken back perhaps

Ken should get his hurricane kick super back

Guile should get the sonic hurricane from alpha

Balrog (Boxer) had the corkscrew blow in alpha

Bison (dictator) should either change up his ultra by having it look like his level 3 knee press super in CVS or get a pure Super Psycho crusher super

Akuma should get his ground pound energy super or his vertical hurricane kick super

Honda should get a super Ochio throw like in alpha

Cammy should get her Killer Bee super back.

Rose should get her level 3 super from alpha, her awesome auto combo into super soul throw back, if not her soul illusion (maybe make it an auto combo or grab utra)

Gen has it good already.

Rufus, not sure, i like his current ultra, maybe give him another super, don't know what it would be though...

Vega (claw) should get his move where he tossed you up so you land on his claw move, i thought it was called the Bloody claw in alpha.

Don't care about chunli, dan, fei long, gouken, sakura, viper, sagat.

Gen- He should have that Dizzy-timer Super. Seriously, for him to be such an old Master of the arts he should be more of a threat........Or should I say, more dangerous than he is now. Plus, that is just one of the coolest Supers in Alpha. 

Guile-Huge Close-range sonic boom

Chunli-Huge close-range projectile

A Psycho Crusher Ultra for M.Bison/Dictator that works as a reliable move against air especially. Something along the lines of Seth's Ultra which can grab a lot of people that jump over his Sonic Boom's, but obviously shorter range for M.Bison/Dictator.