In American football and Canadian football, a quick kick is any punt made under conditions such that the opposing team "should not" expect a punt. Typically this has been a kick from scrimmage from a formation that is, or resembles, one usually used other than for punting, or at least not resembling the one usually used for punting. Typically it will also be on some down before last down (last down being 3rd in Canadian, and, since 1912, 4th in American football), unless done from a formation usually used for place kicking; if opponents begin to anticipate quick kick on next-to-last down, then it may be done on a previous down.
The purpose of a quick kick is the same as that for all punting, but with additional hope of:
- preventing a runback (return) of the ball by the opponents,
- additional distance by the ball's bouncing or rolling instead of being fielded by an opponent, and
- (where legal) recovery and retained possession of the ball by the kicking team.
The disadvantages (required for the punt to be unexpected) are one or more of these:
- earlier sacrifice of possession of the ball, or sacrifice of a kick at goal (field goal);
- greater exposure to the kick's being blocked by an opponent (although that may be mitigated by its being unexpected), or inadvertently by a teammate;
- sacrificing distance or accuracy by need of being done quickly; and/or
- being done by someone other than the team's best punter.
More likely 
Factors that make a quick kick more likely:
- the play's being in a team's repertoire (practically a necessity for any play's likelihood)
- long distance to go for a new first down
- the other team's not showing anticipation of a quick kick, as by dropping a safety player far back
- being close to one's own goal line
- being close enough to the other team's goal line that a field goal attempt is credible, but far enough that its success is not likely
- current or historic rules allowing for the kicking team to recover and retain possession of the ball; see onside kick
- the team's having a player good at both punting and other backfield roles
- the team's not having a good specialist at punting
- conditions that make long drives (moving the ball in continuous team possession) unlikely
- a strong wind blowing either with or against the team; a headwind would encourage a low kick which, if expected, would get quickly to the other team for a runback; a tailwind could allow an unfielded kick much extra distance
- hard playing surface, allowing extra distance via bounce
- the punter-to-be's lining up a yard or so deeper in formation than that back's usual position, (sometimes concealed by other backs' lining up deeper too) or going in motion by backpedaling
- fashion in the circuit in which the game is played
- to confuse the other team
If a team uses the quick kick a lot, surprise can be maintained only by their also having a fake quick kick play. One type of such play is the equivalent of the Statue of Liberty play for the forward pass: the ostensible punter holds the ball out as if to drop it, then hands it to a teammate stepping behind or in front of him.
The quick kick is usually done from closer to the line of scrimmage than an ordinary punt. For approximately the decade of the 1910s in American football, the rules discouraged the quick kick by requiring that the ball be kicked from at least 5 yards behind one's line of scrimmage. Because of the closeness of the opposing team, the approach the kicker uses before dropping the ball for a quick kick is often designed to decrease the distance forward that the punter will step, and/or to reduce the time of the approach. One such technique is the "rocker step", in which the punter first steps backward and then rocks forward. Another is to take a somewhat sideways approach, leaning and kicking somewhat "across the body"; for a right-footed kicker this means approaching toward the right while leaning left.
A quick kick made relatively close to the opposing goal line is often executed by a technique called a "pooch punt", which is a more controlled kick. A typical last down punt or a punt taken as a free kick is done with the emphasis mostly on maximizing distance.
Quick kicks are relatively rare in American football, but they have never completely disappeared. Quarterback Randall Cunningham made 20 quick kicks during his career, including one of the longest punts in NFL history, 91 yards, in 1989. [correction: while Cunningham occasionally did quick kick, this was not a quick kick. The Eagles' punter had been injured and it was a standard 4th down punt] Bear Bryant was known to have used this on third downs when up big or as Kenny Stabler once said "I wanted to see how our defense could do".  Another, more recent example is that of Kellen Moore of Boise State University against Louisiana Tech on October 26, 2010, when Moore delivered a 54-yard punt.  New England Patriots quarterback Tom Brady performed a quick kick punt on 3rd & 10 in the final quarter of a blowout against the Denver Broncos, in the divisional round of the AFC playoffs, on January 14th, 2012.