The simplest way to dash cancel is to jump. Characters who have good aerial attacks, such as Meta Knight and Jigglypuff, are able to benefit the most from this. Some of the momentum from the dash is carried into the character's jump, so those with fast running speed, like Fox and Sonic also benefit. It is also possible to jump cancel into a grab, or, if the player taps up to jump, an up smash or up special.
Crouching is available in Super Smash Bros. 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 sidestep, but also a grab without the normal lag of a dashing grab. Respectively, in Super Smash Bros., a shield grab can also be used for dash-cancelling when A and Z are pressed simultaneously while dashing.
In Smash 64, when initiating a dash, quickly tapping the opposite direction before the initial animation ends causes the character to pivot while sliding forward. This gives characters like Captain Falcon, who has a long, fast initial dash animation and a weak forward aerial, significant approach improvement in his back or up aerial. This also applies to Fox's back aerial (a sex kick which is more powerful when implemented well than his forward aerial) as well as Samus's (whose back aerial is a very powerful kick and one of her few reliable finishers, in contrast to her overly weak, low range forward aerial).
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 often has more lag than the up smash. Because smashes 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 and Smash 4 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 to an up smash.
Down smash 
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 cancelled into crouches in Super Smash Bros. Ultimate, cancelling a dash into any attack is a built-in mechanic, meaning that down smashing out of a dash is possible.
While it is not possible to slide with the down smash (in Smash 64/Brawl) and the side smash while dashing, some characters can slide while using their down and side smashes by doing them while walking at their top speed, Ice Climbers for example.
The player can exit a dash using their side or up special moves (provided the latter is also jump canceled) and exit a run with any special move, which is very useful for approaching. Projectile-based attacks like the Fireball can be very useful when done while dashing. Many special attacks also have good stunning ability, which allows follow-up into other attacks.
A universal buff in Ultimate is the ability to dash cancel into anything besides crouching. This allows characters to more effectively punish and approach without having to first cancel their dash into a shield or crouch. Simon and Marth can surprise foes by with their fast and disjointed jabs, tilts, and smashes, and Little Mac can better utilize his strong ground game now that he has more ways to pressure opponents with his ground moves. Characters can also pivot before attacking in the direction they were running in, exploiting the skid to extend the range of their attack.