The teleport is a glitch-technique in the original Super Smash Bros. that results in a short teleportation forwards. Only Samus, Fox, and Jigglypuff have this ability. Because the technique requires the user to input a jump, at the end of the technique, the teleporting character either ends up in the air, goes off a ledge, or uses a jump cancelable attack. Samus and Fox's teleports are much shorter than Jigglypuff's.
Unlike the wavedash, the teleport is confirmed as a glitch. Because of this, the phenomenon cannot be explained with game mechanics alone. However, it is known that the teleport lasts as long as the character is in the pre-jump animation, and since Jigglypuff has a longer delay before jumping than Samus and Fox, its teleport lasts longer and goes farther.
Performing the technique
The teleport is performed by first starting the normal dash (as opposed to the initial dash), smashing the control stick in the opposite direction, and jumping three frames afterwards. The jump can be canceled by an up special, up smash, or down special (Fox and Samus only).
There are two common methods of performing the teleport. The first method is to dash, smash the control stick back, and then hit the jump button. The second method is to dash, and then make a downward 270-degree arc with the analog stick. It is considered easier to follow up the teleport with a short hopped aerial using the first method and easier to follow up with a jump canceled attack using the second.
Because this technique gives a sudden spurt of speed, the teleport can be used for movement. When coupled with aerials or other attacks, teleporting can be used as an approach. Both Samus' and Jigglypuff's neutral aerials have good range, and all three characters' down aerials are good combo starters. Samus' Bomb is also a good option (known as the bomb teleport). By coupling the teleport with Jigglypuff's Rest, the player can land surprise hits on an unsuspecting opponent. Jigglypuff can also combo into this technique using moves such as dash attack or back aerial. Also, performing an up smash after teleporting with Fox can be a pretty helpful finisher for aerial combos as well as dealing with tech-chasing.
If the teleport goes off an edge, the character will end up off the edge in free fall. When this is coupled with an aerial, it can be very useful against a recovering opponents. It is especially effective with Samus' down aerial and Fox's shine, since the former is a very quick meteor smash (plus one of Samus's very few reliable KO options), and the latter allows the shine spike technique. Jigglypuff can also perform a slightly faster edgehog than jumping backwards to grab the ledge by teleporting off the ledge and jumping towards it.
Normally when teleporting, the character dashes, then goes into the pre-jump animation while sliding, and then jumps once the animation is over or falls off the edge if the teleport goes off an edge. The jump after the animation can be canceled by using an up smash or up special move. With most attacks jump canceling results in canceling the teleport. However, when the teleport is canceled with Jigglypuff's up special (Sing), the momentum will stay throughout much of the attack and the teleport lasts longer and travels farther than normal.
Fox using an up smash out of a dash, without a teleport on the left, and with a teleport on the right. The additional distance given by the teleport can clearly be seen.