Hitstun is the period of time after being hit that a character is unable to act outside of directional influence or teching. Hitstun received is a function of knockback so it is essentially also linked to the distance travelled before action is possible. When a hit deals too low of knockback to lift the opponent off the ground, hitstun is equal to the length of the flinch animation, while at higher knockbacks it is a straight multiplier of the knockback received. Each Smash game has a programmed value that is multiplied by the amount of knockback received to determine the amount of frames a character is locked in hitstun after being hit (for example, Melee has a hitstun multiplier of x0.4, so a hit that deals 100 units of knockback will leave the target in hitstun for 40 frames).
Hitstun is an essential component of combos, with the point of a combo being that the target is trapped in the hitstun of consecutive attacks. As a result, games that have more hitstun for equivalent knockback open up more potential combos.
The amount of hitstun in the original Smash is notoriously much higher than in the subsequent Smash games, being a x0.533 multiplier. The multiplier is so high that long and highly damaging combos are commonplace, with competitive matches being heavily centralised around them, and zero-death combos not being uncommon for most characters. In fact, every character in the game except Samus is capable of pulling a zero-death using their normal moves. The commonness of zero-deaths in this game is one of the primary reasons why competitive matches are played with 5 stock, which is more than Melee, despite the game not being as fast-paced as Melee.
The amount of hitstun in Melee is a significantly lower x0.4 multiplier, making Melee a less combo oriented game, and zero-death combos a rarity. However, with the increased falling speeds, and generally faster and more varied movement, combos remain frequent, though generally more difficult to pull off consistently.
Brawl has the same hitstun multiplier Melee has. However, when hit, characters can now air dodge after 13 frames and attack after 25 frames out of hitstun, regardless of the actual amount of hitstun they sustained; this new mechanic drastically reduces the amount of actual hitstun characters have to sustain upon being hit, especially at higher knockback (for example, while a character sustaining 100 units of knockback in Melee will be in hitstun for 40 frames, in Brawl that character will be in actual hitstun for only 13 frames if they air dodge or 25 frames if they attack, and if that knockback value is doubled, while the Melee character would sustain an inescapable 80 frames of hitstun, the Brawl character will still only sustain 13 or 25 frames of hitstun). This drastically reduces the amount of true combos, and makes the only attacks that can truly combo being those that deal very low knockback while having low enough ending/landing lag to followup within 13 frames before the opponent can air dodge (such as chain throws, Meta Knight's up aerial, and Sheik's forward tilt). Any other attack that deals a slight bit more knockback or has a slight amount of more ending lag will require the player to successfully read the opponent's action to successfully followup. This new mechanic also allows launched characters to act before their knockback wears off, which allows characters to perform certain actions during knockback to reduce their aerial momentum, allowing them to survive blows that would have otherwise KO'd.
The much slower falling speeds, loss of L-cancelling with most aerials not having their landing lag compensated, and generally slower movement also reduces the amount of possible combos, though the effect of these is miniscule compared to the ability to act so early out of hitstun.
This new mechanic is one of the most controversial additions to Brawl, with detractors criticising it for making true combos rare and making it impossible to truly combo with moves that deal anything beyond very low knockback. This eliminates the comboing ability of characters that relied on higher knockback moves with faster mobility to combo (Captain Falcon being the most prominent example), allowing characters to survive longer than what was intended through momentum cancelling and significantly increasing the chance of getting punished for landing a hit. While some players argue in support of the mechanic, such as by arguing that players should have to successfully read their opponent's actions to get successful followups and that opponents should have means of escaping combos, the majority of competitive players, even those who prefer Brawl over Melee, see the mechanic as a negative addition to the game. As such, those who mod the game usually remove the mechanic unless they intend to keep the vBrawl engine intact (such as Balanced Brawl), and all major mods, except the previously mentioned Balanced Brawl, have removed the mechanic completely.