All pitches that have movement (aside from their normal flight towards home plate) take advantage of differences in air pressure on the different sides of the ball. These differences are caused by the rotation of the ball. For instance, let's say a pitch from a right-hander has rotation from outside to inside, that is, the part of the ball that is toward the third-base line moves toward homeplate and then back towards the first-base line (and repeat, until the pitch is caught.) Now lets look at the third-base side of the ball. Friction from the surface of the ball and from the threads pushes air in the direction the ball is spinning, forwards towards home plate. This air then hits the air that is being displaced by the ball's forward motion toward the plate, and creates a localized area of high pressure. Slow moving air = high pressure. On the other side of the ball, the air that is being pushed by friction -- from the surface of the ball due to its spinning motion -- is being pushed backwards, back towards the pitcher's mound. This air does not collide with the air being displaced by the forward motion of the ball, and, rather, it is essentially going in the same direction around the ball. This creates a localized area of air moving at high speed, and air moving at high speed means a low pressure field is created. So, now we've got a high pressure field on the third-base side of the ball, and a low pressure field on the first-base side of the ball... so, naturally, the ball will have a natural tendency to move from right to left from the pitcher's perspective, from the third-base line to the first-base line. All pitches with "motion" generate that motion based on this principal.

The pitcher throws the ball with a sharp 2 o'clock to 8 o'clock wrist movement at the end of the delivery (imagine locking a deadbolt latch while throwing your hand downward). This gives the ball a downward movement when it reaches the plate. Curveballs don't actually move much from side to side, they tend to move mostly straight down, but their 'hook' is delayed until the end of the throw which makes it more difficult for the hitter to pick up on. The only pitches that have dramatic lateral movement are the screwball and the knuckleball, both of which still mostly move downward. The screwball is a reverse curveball (imagine looking at a watch on your throwing wrist while moving your hand downward). It's extremely hard on the arm for most pitchers, which is why it is rarely thrown. A pitcher with a sidearm or submarine delivery can sometimes get a sharper lateral motion on a slider or cut fastball.