Many football fans would be surprised to know that the drop kick is still officially on the books in the NFL. Many more think it's another term for the punt. Still others are only are aware of the phrase in terms of the band The _______ Murphys or as something a devout stereotype might fervently wish for Jesus to do to them through the goalposts of life.
To drop kick, you drop the ball on the ground and kick it when it bounces. In American and Canadian gridiron football it was used to kick the extra point after touchdown; also as a surprise move to kick a field goal (so Wikipedia tells us). It is an important skill in rugby. But since our football was made pointier at the ends to facilitate passing, its bounces have become less predictable, and a drop kick may never get to the "kick" part. The last successful drop kick was done by Doug Flutie in 2006; it was his last game ever and they called it for laughs. The last successful drop kick in the NFL prior to that was in 1941.
There are strong disincentives at play with the drop kick. If you try it and the ball bounces away from you, it is a fumble; if you kick it after more than one bounce it is an illegal kick. It also is no longer an important tool for the field goal anymore. The league has penalties now to protect the kicker on a field goal attempt, and those along with other rule changes mean that having to pretend you're not going to kick a field goal when you are is alien to us. Much more common is setting up for a field goal as a fake for a pass or run, but even that's rare.
Also, nowadays if you try a drop kick and fail, you look like a big stupidhead. If you succeed you're a genius, sure, but who wants to roll the dice on that? No one practices this play anymore; what are the odds of pulling it off? Even Randall Cunningham, one of the greatest athletes to ever play QB, a guy who screwed my Giants over once with a 91-yard punt, never pulled off a drop kick.
So I doubt we'll see a return of the drop kick in today's Super Bowl, but it would be great if we did. Sorry, sad football; we're much more likely to see an underinflated football than a drop-kicked one, and with the whole world watching New England's balls, that's not going to happen either.