The first offensive scheme I want to discuss is my personal favorite, the spread. The spread does just as it sounds, it spreads the defense out. This involves having at least 3 receivers split out (away from the line) at all times. This works because the defense also has to spread their coverage out to defend it. Because of this you can also have a lot of success running the ball, with fewer defenders in the box. Also, you can do more read option type runs with the defense as spread out as it is. The key to running the spread well is good having good athletes to play at the receiver positions, and a quarterback good enough to get it to them. This is important because all of the wide-outs need to be a threat to the defense, making the defense devote players to stopping each one. Another benefit of the spread is it opens up the field. There is so much more you can do in the screen game, and vertical passing game with a spread out offense. This also can be a negative as it is much harder to fool the defense, because they can see much more of what you are doing. Also, you have less blockers in the box, which means it is harder to run right at the defense.
The second scheme I will discuss is the I-formation, and those formations similar to this. This is more of a tight formation with generally a tight-end on the line of scrimmage. The I-formation utilizes a full back behind the quarterback where-as the spread does not. This formation is used for more of a power running style with a fullback leading the way. Passing in the I-formation usually involves play-action and roll-out passes. In these passes the receivers all go to the same side of the field, making the quarterbacks decision easy. The key to the I-formation is being able to run the ball. If you can get about 4-5 yards per carry, then the defense starts getting drawn in, that's when you hit them with a play-action and generally get large chunks of yardage. Also, the I-formation uses a tight-end (most of the time) as an added linemen in the running game, and a additional receiver in the passing game. This player must be versatile for it to work, as he must be able to handle blocking a defensive-end, and be skilled enough to get downfield and catch passes. This formation is called an "I" because the quarterback, fullback, and halfback are in a straight line perpendicular to the line of scrimmage. For formations similar to this the fullback goes to the strong or weak side, but the same types of plays are run. The negatives to the I-formation come if you are unable to run the ball successfully, because then the play-action doesn't work and you won't be able to move the ball at all.
The third and final scheme I will discuss is the tight formation. This can involve a various amount of running backs, with generally 2-3 tight-ends, and 0-1 wide-outs. This formation involves fast-paced quick hitting run plays over and over again. There is usually quite a few fakes involved as well. Passing out of this formation is very rare, but can be very successful because of how infrequently it is done. For this formation to be successful you have to be physically dominating up front. Because the defense knows what your doing, so you have to be able to be better then them. This is also it's weakness because if you are unable to run, there isn't much you can do.
The three schemes I discussed above are the spread, I-formation, and tight formation. Like I stated in the introduction offensives schemes will usually utilize all of these formations along with a variety of others, depending on the strengths of your team. This is what the most successful offenses are able to do. If you are unable to beat the opponent at the line of scrimmage then you need to be unpredictable. This calls for running a variety of formations in your offense.