I've managed to figure out all the moves of ken (after properly mapping the controls) and it turned out to be the same (almost at-least) for many others. It wasn't really easy figuring them out.
Make sure you have the movement controls as wasd, uio as punches, jkl as kicks, y as triple punch and h as triple kick(or whatever its called). The rest where ever you find convenient.
The ultra combo for Ryu is sd sd and y. Check how the movement is in the command list and cross check for a similar movement in the below mentioned characters.
Here's a list of players having a similar controls(i.e.combos) scheme -
Sagat,Ken,Ryu,Sakura,Dan,Abel,Viper & Dhalsim.
Note: some characters may have a slightly different movement for certain combos.
Thanks to that, I've managed to finish the game as Sagat,Ryu,Ken,Dan and Sakura in medium difficulty and yes, I am aware of every move of those characters.
Edit: You can pull of El Fuerte's ultra combo as well.
Also, for shoryuken and similar moves in other characters - s(hold) tap d twice and press any punch/kick move (depending on the character).
The dragon punch input in SF4 is notoriously easy to trigger--down-forward down-forward is all that's needed to trigger it, because the game counts the first df for both the forward and the down input of the DP motion, forward, down, down-forward. Since you are often jiggling through the down inputs while crouching, it's easy for the game to interpret a dragon punch. You're not alone, many people have this problem and give the SF4 games flak because of it. I think the square stick gate on TE sticks exacerbates the problem slightly, because it can be difficult to get a straight horizontal input, as opposed to a diagonal one.
When going for things like cr.MK xx fireball, a dragon punch can happen when you hit the button while the stick is still on down-forward, instead of forward. Be sure to follow through with your fireball motion, making sure you hit forward, and then delay the button press just slightly so that you are definitely hitting it after the motion.
In fact, it can help to go all the way from down to up-forward, making a 135 degree arc instead of 90. This explicitly makes sure you hit the forward input. This is useful in a lot of cases when the game has trouble distinguishing inputs. For example, it's especially helpful when doing M. Bison's Ultra 1, which has a very bad habit of coming out as a teleport. Instead of charge back, forward, back, forward + kicks, you can do charge back, forward, back, up-forward + kicks, which makes sure that the game sees the forward input instead of down forward.
Best Answer
Along with the 360, there are certain ultras, such as Zangief's that require a 720.
The not so well known knowledge for beginners is that, as Stof mentioned, the game is very tolerant for such moves. What you only really need to perform, is a lazy 270 rather than the complete 360 before it recognizes the move as a full circle.
The standard accepted way of performing such a move is a HCB*, UB.
You'll want to hit the punch button as soon as you reach UB to prevent the jump.
For a 720, you can do: HCB, UB, HCB, UB. The second HCB to UB needs to be performed extremely fast before Zangief has a chance to jump. Zangief has a certain number of frames before the jump command actually kicks in, and as long as a move is performed within those frames, he will not jump. (I believe the number is 6).
There are three standard ways of pulling off a 360:
Perform a normal attack. This is usually the preferred way of doing the move. Street fighter allows you to 'buffer' an attack up while doing another motion, and this is very similar to how to buffer up a charge attack as well.
Perform a move as you are getting up. There are risks and rewards associated with this type of move, its up to you to decide.
The least preferred method is to perform the circle move as you are jumping, but this is the most easy to perform for beginners, especially the 720. However, this is a dead give away that you are trying to perform such a move.
For additional tricks, look up the "Walking 720" for ways of pulling off the move.
*HCB = half circle back, UB = up back