There are many possible formations that fall within legal guidelines. I use 12. Twelve is plenty for my offensive scheme because each formation can be modified by sending one of several players in motion, or simply slightly shifting one or more players. Also many formations can be run from the shotgun, or not.
For these reasons explicit, detailed, single diagrams for each formation serve little purpose. Instead let's look at all of them at once, and then briefly discuss each.
The basic Pro Set (shown here as Pro Left) calls for the TE left with both flankers. The opposite WR is split to the right. The QB is under center, with one running back. This formation is extremely popular because there are five eligible receivers, the inside flanker or the running back can go in motion, or the formation can employ the shot gun. This formation is equally effective for the run or the pass.
The Veer and the "I" are equally popular for the same reasons, but employ two running backs. This strengthens the running game by adding an additional running back to the overall scheme.
The Power "I", Full House, Wing-T, and the Wishbone (optional) all can utilize two tight ends and three running backs making them strong running formations while still keeping 5 receivers eligible for the pass.
The Twins set calls for two receivers to the same side with the tight end to the opposite side, in tight or split wide. Two backs are in the backfield, both eligible to be set in motion.
Tripps simply calls for one of the backs to join the wide receivers forming a trio of wide outs to the same side. Again, the tight end (to the opposite side) can be optionally split wide.
Quads call for four receivers to the same side, two up on the line with the other two stacked behind them. The back two receivers can be offset from the forward two. Slots call for two receivers to each side with the outer two up on the line of scrimmage, the inner two a step back.
The Spread formation lives up to its name. Each lineman increases his splits from one to three (4, or 5) yards. There are two tight ends, two flankers out wide, five linemen, a back and a quarterback. There are eight lanes between the nine forward players. If their respective gaps are 5 yards apart, you "spread" the offense out over 40 yards. If the defense responds by splitting out wide with the offense, the quarterback can hand off to the back who has widened running lanes. If the defense does not spread out with the offense, there should be mismatches to the wide sides of the field for the pass.
Each of the formations can have a variety of looks to the defense. For instance, every formation has a 'mirror' side. Tripps right can be run as Tripps left.
All twelve formations can send a player in motion.
Eight of the twelve formations can utilize the shot gun formation where the quarterback lines up 5 to 7 yards deep in the back field as opposed to taking the snap from under center.
Also, many of the formations can take on an entirely different look simply by shifting one or more players around. An excellent example of this is the Wing-T formation. The Wing-T can be run as Wing-T left with the back to the right (1), left with the back to the left (2), left with the back in motion (3), left with the Wing Man (purple dot in the diagram) in motion (4), these options 'mirror' plays (5,6,7,8), with or without the shot gun (9,10), or from the Double Wing-T with or without the shot gun (11,12). So, in fact, the Wing-T formation (one of twelve) can have twelve different, distinct looks for the defense. Multiply these results by the total number of possible plays which can be run from most of the formations and one can begin to sense the vast number of "looks" the offense can give a defense. Add an intentionally diverse, tricky snap count and the offense should be able to keep the defense on its heels further expanding the play calling options for the coaching staff.