- Not to be confused with dash attack canceling.
Dash-canceling is a technique in the Super Smash Bros. games that, hence the name, cancels a character's dashing animation, which can allow them to perform other actions from it. There are several ways to do this.
The simplest way to dash cancel is to jump. Characters who have good aerial attacks, as well as characters with fast air speed values generally benefit greatly from this. In Super Smash Bros. Melee but not in other Smash games, some of the momentum from the dash is carried into the character's jump, which can benefit characters with fast running speeds. It is also possible to jump cancel into a standing grab (Melee only) or an up special or up smash (although jump canceling is not necessary to perform an up smash in Super Smash Bros. Brawl, Super Smash Bros. 4 and Super Smash Bros. Ultimate, or an up special in Ultimate).
Crouching is available in Melee during the run, which starts anywhere from frame 8 to frame 19, depending on the character. It is thus called run-canceling. Canceling with a crouch causes the character to slide a little bit, almost like wavedashing. From crouch, all attacks can be used immediately. Only movement, especially walking, dashing and platform-dropping, are not possible immediately. For these, waiting until the end of the crouch animation is necessary.
Putting up a shield allows the character to do any defensive techniques involving the shield while the game considers one to be standing. This not only allows the character to do a roll or spot dodge, but also a grab without the normal lag of a dashing grab, in addition to jumping. Respectively, in Super Smash Bros., a shield grab can also be used for dash-canceling when A and Z are pressed simultaneously while dashing.
In Smash 64, Melee, Brawl and SSB4, when initiating a dash, quickly tapping the opposite direction before the initial animation ends causes the character to pivot while sliding forward. In the former two games, the absence of the reverse aerial rush technique can make pivoting necessary in order for characters to approach with back aerials, for example. Another use is to perform grounded attacks other than dash attacks, dash grabs (standing grabs in Smash 64 because dash grabs do not exist in that game), up smashes and special moves easily, especially ones that are useful approaching/combo tools or whose hitboxes begin from the back. Yet another use is as a general movement option for spacing. This technique does not exist in Ultimate.
The small delay provided by an initial jump makes it possible to execute an up smash while running. The result is the character sliding a little while performing their up smash. This is usually a good alternative to using the character's dash attack, which sometimes have more lag than the up smash depending on the character used. Because smash attacks can be charged from Melee onward, this allows for execution of the slide smash technique. A dash-canceled up smash is made much easier in Brawl, SSB4 and Ultimate as because C-stick inputs are read as Tap+A inputs, it is possible to simply flick the C-stick up at any point in the run (including the initial dash) to an up smash.
Down smash 
In Melee, within the first few frames of a crouch, it is possible to press the attack button to interrupt and perform a down smash, which allows the player to slide while using the down smash if a dash is used first. This is still considered hyphen smashing as the character will slide for a short distance if charged. Down smashes are also useful approach tactics when used in this manner because they tend to sweep the ground. Unlike using the up smash though, the down smash will not cause all of the characters to slide, as some down smashes negate momentum like Links. This technique is not available in Smash 64 and Brawl, because it is not possible to cancel the dash with a crouch in these games. While dashes cannot be canceled into crouches in Ultimate, canceling a full run into any attack is a built-in mechanic, meaning that down smashing immediately out of a run is possible, but not out of an initial dash.
While it is not possible to slide with a down smash or a forward smash while dashing in Smash 64, Brawl or SSB4, some characters can slide while using their forward or down smashes by doing them while walking at their top speed, with an example being the Ice Climbers. This is due to those characters having low traction.
Forward smash 
It is possible to cancel a dash with a forward smash in all Smash games through the use of the small step forward smash mechanic, which allows a 3 frame window to cancel the dash into a forward smash in the same direction as the dash, and a 1 frame window to forward smash in the opposite direction.
In Ultimate, the run-canceling mechanic allows forward smashes to be performed out of a full run by any character.
The player can exit an initial dash using their side or up special moves (provided the latter is also jump canceled, though that is not necessary in Ultimate) and exit a full run with any special move, which is very useful for approaching. Approaching attack special moves, as well as certain disjointed or projectile special moves, can often be useful if done out of a dash or run. Many special attacks also have good stunning ability, which allows follow-up into other attacks.
A universal buff in Ultimate is the ability to cancel a full run into virtually any move, as opposed to only up smash, special moves, dash attack, dash grab, pivot grab, jump, shield, roll or spot dodging. This benefits characters with fast running speeds, characters with fast grounded attacks and characters with disjointed grounded attacks the most. It also benefits certain characters with down tilts that slide them forward along the ground, enabling those characters to use their down tilts as effective alternatives to their dash attacks as approaching attacks. Characters can also perform virtually any attack out of a run turnaround as well, including up smashes without needing to jump first; additionally, the ability to perform any move out of a run turnaround enables characters to slide forward while performing a tilt attack or forward smash in the direction they were running in.