Capcom has added in several "shortcut" motions and tricks over the years to their Street Fighter games. Usually they simplify a motion, or give players a bit more leeway in which directions or buttons they have to push to make a special move come out.
In Street Fighter 4 the most prominent and notable shortcut motion is for Dragon Punches (DPs). Rather than the traditional motion, the one shown below will work in its place.
That means you can stay in an offensive crouch position and with a very quick and smooth flick of the joystick (or D-Pad) have a Shoryuken out there without having to press towards first. If you struggle in combos or in matches in getting DP motions out, try the new motion. It may help you out quite a bit, especially for those of you using a square-gated joystick.
The motion listed above also works for reverse DPs such as Fei Long's Flame Kick. Also be aware that this trick only works in SF4 currently.
One neat trick that this shortcut offers you is an anti-crossup Dragon Punch. While you can stay in a crouching position, simply shift your joystick over like this:
You have to wait to press the Punch button until the opponent is on the other side, but it is a great way to punish crossup attacks.
Contributions to this guide by ShinobixTC and Nyoro.