Time was when each kicker was not a specialist but a regular Joe on the team; all of the best kickers in the NFL before 1950 were important members of the offense or defense. Lou "The Toe" Groza, of the Cleveland Browns, was the most famous, his reign peaking during the Browns' domination from 1950-55. His day job on the team was a beefy offensive tackle, so he carried maybe 250 pounds, an unofficial record that would stand until 2000 when the Raiders drafted 255-pound Sebastian Janikowski in the first round.
Of course, he was more well known as a lineman than as a kicker. He was considered one of the best in the game, and reputedly allowed fewer sacks than any other lineman in the modern era. Unfortunately, there is no way to verify this claim, since sacks were not kept as an official statistic until 1983. He was elected to the Hall of Fame primarily on the basis of his tackle play.
Groza's approach to the kick was simple: stand three steps behind, stare at the ball, lock your ankle and toe the sucker. Very straightforward and simple. He set a record for accuracy. Other kickers naturally copied his style and, for the first time, the field goal became a legitimate scoring threat for a team once its offense drove into the other team's field.
But the game was changing, and the kickers along with them.
Football evolved from rugby and inherited the ball used in that sport. It was (and is) a fat ovoid that widens very quickly at the ends and contains a lot of bounce. Great for kicking, which happens frequently in rugby, but sucky for throwing, which happens frequently in football. So as the forward pass was introduced to the game in the 1910s-1920s, players realized the folly of trying to accurately toss a almost-round ball and complained to the various rules committees. Over the next couple of decades, the officially sanctioned shape of a football became longer and thinner. It became easy to grip with one hand and to throw with a spiral, which greatly improved accuracy. Teams slowly made the forward pass a major part of their offensive strategy and techniques were developed for catching a thrown ball.
Kickers, on the other hand, began to realize that the old way of doing things was not working well anymore; accuracy was down and offenses started attempting fewer field goals. The new, thinner ball did not offer a large space where one could toe it with confidence. Techniques were adjusted to compensate, but nobody of the new generation could match a performance like Groza's. The situation looked grim.
Enter Pete Gogolak.
Gogolak was a kid from Europe who moved to the U.S. during his high school years. Like lots of other European kids, he loved soccer dearly and quickly won a starting spot on the school team. A friend who played football was watching him blast soccer balls the length of the field and suggested that he try his hand at kicking this funny-shaped brown thing. After reviewing the important point that the goal, to count, must go over the crossbar instead of under it, he set up and booted it in the soccer-style manner that was natural to him. It didn't go through, but it did sail in a long, low line drive, and Gogolak decided to practice on it.
He got it down and decided to try out for the team. The coach looked askance at his weird style, but let him handle the kickoffs that year because he was able to put it out of the endzone every time. In his senior year, he took the job full-time and set school records for accuracy, distance, and popularity (he was the first kicker elected captain of his team). His career continued, eventually leading him to the New York Giants. Other kickers saw the accuracy of his method and copied it, thus reestablishing the place of the field goal -- and the kicker -- in the strategy of football.
The toe-kickers were not entirely out yet, though. Tom Dempsey, a man afflicted with a severe form of clubfoot from birth, had a foot maybe half the size of the other with a broad flat surface where the toes would be. Combined with his strong leg, he set the NFL record for distance with a 63-yard field goal in 1971, a mark that as of 1999 he shares with the soccer-style practitioner Jason Elam of the Denver Broncos. Soon afterward, Dempsey left the game and the toe-kicker disappeared from football entirely as the soccer-style players mastered the art.
We're not likely to see another change in kicking style without a change to the equipment of the game again. Current standards insist that a kicker be almost automatic from 30 yards in; 80% from 30-40; 70% from 50-40, and 50% from 60-50. (These are just approximate numbers, kids.) Irrespective of style, anyone who manages these numbers with his foot has a future in the sport.