The first and foremost reason why players hate those Goddamned Bats, and the means by which many Ledge Bats send players plummeting to their doom....
Knockback is a Video Game simplification of basic physics where if a character is struck by an attack, it will physically push them aside some measure of distance* Sometimes even allowing them to get to places they normally can't. Modern games featuring full physics engines can incorporate numerous factors (relative mass, speed, gravity/wind, etc.) to calculate the exact force and direction of it, while older and simpler (and by extension, Retraux) will use extremely simplified rules, such as whether the attack originated from the right or left of the player.
But regardless of its technical implementation, its actual effect on gameplay can be sorted into rough categories:
Flinching: Short-term knockback yields little more than a 'flinching' animation and may interrupt whatever action the player was performing (a combo or Charged Attack, say). The knockback otherwise does not impede or interfere with player movement or control.
Knocked back: The most common manifestation of knockback interrupts the player's action and momentum and pushes them back a short distance (perhaps one or two steps); the character recovers their footing quickly, and the player is able to resume action in short order.
Knocked down: In its extreme manifestation, the player's character may be knocked back a significant distance, and the player is unable to control them until the character comes to a stop and is able to get back up onto their feet again.
The final segment of the Final Boss of Beyond Good & Evil suddenly ramps up the effects of the game's knockback—while present-but-negilible before, even a small attack will now result in the heroine getting totally decked. During one sequence of attacks, it is entirely possible to get "stunlocked" and make the fight Unwinnable until you inevitably die and get sent back to the checkpoint.
Deadly Towers has Prince Myer get knocked in whatever direction is opposite the way he's facing quite a distance without a way to stop himself. Unfortunately, this game also features Bottomless Pits...
Explosive weapons and melee attacks in Iji cause knock back, while weaker weapons cause flinching. This applies to both enemies and the protagonist. The knock back from some weapons reaches Blown Across the Room levels - Many secrets in the game can only be obtained by taking advantage of this.
Many fighting games feature "grapple" and "throw" moves, and knocking an opponent out-of-bounds can trigger a Ring Out in various titles.
Some fighting games like Guilty Gear have a pushblock mechanic that allows a defender to enter a state where the opponent is pushed away when their physical attack is blocked.
The Super Smash Bros. series is based entirely aroundRing Outs; characters do not have depletable HP but instead receive greater knockback as they take damage, until they are inevitably thrown from the arena.
Some games such as later King of Fighters entries take Knockback to an extreme, making some attacks capable of bouncing an opponent off the wall/floor in order to extend combos.
A key game mechanic in Dissidia: Final Fantasy, in the form of Wall/Floor/Ceiling Rush. Essentially—many attacks send the opponent away from the fighter at high velocity. If an attack has the ability to wall rush, and there's a wall somewhere along the victim's trajectory, they'll slam into it for extra damage (base value of one-half of the damage done by the original hit in Dissidia, one-quarter in Duodecim). Interestingly, various attacks have various 'likelihoods' of wall rush—a lot have zero chance of rushing, no matter if your opponent is right up next to the wall/ceiling, some have wall rush for a certain amount of distance (e.g. Bitter End can wall rush, but the opponent recovers if there's no wall for a long way), and a very amusing few (Nightglow, Shadow Bringer, and Cross Slash, for few) basically have guaranteed wall rush—so long as there is a surface to slam into, the opponent will do it—even if the closest wall is hundreds and hundreds of meters away.
In fact, Cloud's fighting style is aggressively dependent on Wall Rushing. Almost all of his skills have a high chance of Wall Rush, and his most basic attacks will generally send the opponent flying into a wall (or enable a chase scene, if the wall is too far away). Abusing this mechanic is his raison d'etre: he's not just hitting you hard, he's hitting you hard, then slamming you into a wall for more damage while he rushes after you to rinse and repeat.
In Skullgirls, there is a feature where your opponent is allowed to break out of an infinite loop if the game notices you performing the same sequence several times in a row. Knocking your opponent hard enough to make them bounce off of a wall will "reset" the loop, allowing you to continue attacking.
World of Warcraft featured knockbacks by various NPC mobs and bosses from when the game was first released, but players didn't get access to them until Patch 3.0, the Wrath of the Lich King expansion, when a small handful of abilities were given to various classes that would knock NPCs or other players back. NPCs don't take falling damage and can run up some sheer cliffs so Knockback abilities are generally underpowered against them, but in certain limited circumstances Knockback effects can be very, very powerful in Pv P.
Humorously, they can get so annoying in dungeons (they disrupt positioning and can knock enemies into reinforcements) that several classes have the ability to turn off the knockback aspect of the spell through the use of a glyph (Mages, Druids, and Shaman, for those who care.)
The flinching ability is available from the start however, in the form of various stuns as well as interrupts.
City of Heroes has three versions: knock back, knock up, and knock down. Almost all melee classes have a power that resists these effects. There also exist enhancements that provide the player with resistance to it, which are in very high demand as most players hate being knocked around by enemies. There also exist enhancements for increasing the knockback in your own powers.
As an action MMO, Dragon Nest practically requires players to exploit the various forms of this trope as even Mooks can easily do the same. Resistance to this trope can be a Gamebreaker especially in PVP.
Star Wars: The Old Republic has it in various forms. From the simple 'interrupt' ability that interrupts abilities being cast or channeled (and preventing it from being cast again in a few seconds), then there are 'stun' and knock down abilities that is as good as it sounds (but also on very long cooldown), to knockback abilities that sends the enemies flying.
La-Mulana utilized significant knockback. Touch even the slightest enemy or brush up against a spike and Lemeza is sent sailing across the room at full velocity, with no ability to alter his trajectory until he lands.
In the sidescrolling Mega Man titles, knockback always occured relative to the direction Mega Man was facing, regardless of the direction of attack. In the "classic" series, it also interrupted charged Mega Buster shots (starting in 5, 4's Mega Buster was more stable), and in 9, Proto Man suffered double the knockback of Mega Man.
The ROM HackRockman 4 Minus Infinity averts this for the most part... aside from the Jumbig, who has an incredibly large amount of knockback. In fact, it's possible to get catapulted into the next screen by touching him at one point in Toad Man's level!
The sidescrolling Super Mario Bros. games generally provided Mercy Invincibility without knockback, which allowed players to short-circuit the fights with Bowser simply by running through him and grabbing the axe at the far end of the arena. This was changed in New Super Mario Bros., where coming in direct contact with Bowser knocks Mario back, away from the switch at the opposite end of the arena.
In the Wonder Boy series (as well as its many ports), Mercy Invincibility only protected the player from further HP loss; it did not protect the player from being knocked back or juggled by repeated attacks.
The rocks in the first game, which were the only non One-Hit Kill hazard, tripped Wonderboy when he ran into one, potentially bouncing him into an enemy or Bottomless Pit.
Castlevania: Symphony of the Night has two distinct types of knockback. Usually, taking damage just shoves Alucard back a couple of steps, but if he takes one hit that depletes half or more of his maximum HP, he goes flying and won't stop until he hits a wall, at which point he briefly sticks to it before falling down. In the special Luck Mode, this severe knockback is what lets you skip the screen where Death steals Alucard's equipment thanks to his greatly lowered stats allowing the Warg's charge attack to do enough damage to trigger it: in normal gameplay, the only time you're likely to see it happen is if Galamoth hits you with one of his more damaging attacks.
The first Flintstones NES game made the player fall back and be stunned for a second when hit, often down the pit. The second game removed the knockback, although the stun effect remained.
The protagonist in Cave Story receives knockback only based on the direction he was hit from. This is an interesting case because while the character receives knockback, you're still in full control, enabling you to affect the distance of the knockback to a certain degree. In fact, the character rarely gets knocked back, but often forward or forward and up. Furthermore, abusing vertical knockback from crashing into a flying enemy is the only way to get a certain item without backtracking (or grabbing the Machine Gun).
In Holy Diver, knockback is a major hazard when fighting enemies near Bottomless Pits, which occur all too frequently.
In Viewtiful Joe and the sequel installment, any hit from a stage obstacle or enemy will knock Joe, Sylvia, or any other character to the ground, which will deduct from your final ranking whenever it happens in a "Just Go For It!" segment of the game, miniboss battle, or boss battle. By purchasing the move "Ukemi" in the game at some point (which requires a hefty amount of coins), with expert timing and a specific button combo, you can recover from the knockback just before you hit the ground and flip yourself back into the air, which recovers a heart in your health meter and rescues your ranking from being lowered. The same can't be said for the higher, insane difficulties that punish you for making any mistakes- Ukemi still recovers only 1 heart, which won't help you in dire straits or save face when you get your ranking after taking eight hearts of damage. Some enemies will actually deliver rapid and brief slashes, such as the ninja, that don't send the player to the ground on a hit, but make them flinch and leave them open to multiple hits until they suffer a legitimate knockback, which are impossible to counter when the player gets trapped in the Cycle of Hurting.
Sonic the Hedgehog 4 has the Final Boss of the Sequel game in an arena where Sonic has to climb up a platforming challenge repeatedly to hit it. If it takes too long to hit the boss, it will spin Sonic and Tails around using gravity and forcibly blow them into a wall, forcing the loss of all your rings.
Nebulus has a variation in which getting hit by an enemy will cause you to fall to the next lower platform, which will cause you to drown if there isn't one. This is actually a useful way to reach otherwise inaccessible platforms.
In Mass Effect 2 when your character is hit by "impact" attacks (Explosive or telekinetic powers) he or she will stumble and move back a step or two. This is completely logical given that they are being hit by a physical force, but this effect is rather egregious when your character is hit while ducking behind cover. In this case, when you are already crouched down on the ground, your character will stand up before they stumble and take a step back. This means your character is deliberately moving out of cover, since they take an independent action (standing up) before they are uncontrollably knocked back by the force, instead of simply falling down or stumbling where they were.
This is the primary criticism of the Geth faction in the Mass Effect 3 multiplayer. Apart from the standard Geth Trooper, every Geth enemy you face has a stun attack. It's especially bad on the higher difficulties, since the Geth Prime fires its cannon in three-shot salvos.
In Skyrim, a power attack will cause an opponent to stagger, and the Unrelenting Force shout will stagger an enemy, or send them flying at it's highest level.
One of the higher tier archery abilities, Power Draw, introduces knockback to arrows, half the time. Needless to say, the ability to stun an opponent at range over and over again is almost a Game Breaker. The only reason it isn't is because it only affects creatures that are about as big as the player; dragons, for example, don't care about knockback at all.
In Diablo II, knockback is a specific effect that can be either part of an attack, or a modifier on a weapon. Knockback is guaranteed to make an enemy flinch and interrupt their attack, but it may take longer to kill enemies in melee because you'll have to keep walking up to them.
In Xenoblade Chronicles, enemies are susceptible to fall damage, so the well-timed use of attacks with knockback on them can shove them off cliffs for an instant kill. Coupled with moves that induce the sleep status (Which are both difficult to dodge, and reduce the affected enemy's evasion to zero), this can allow you to kill enemies that are much higher leveled then you, and reap the overpowered rewards from it. For this reason, bosses are completely immune to knockback. Of course, enemies are also just as capable of doing the same thing to you, and with greater ease, as while your attacks only shove them back a few body lengths, their attacks can send the party flying about five times as far, with the added annoyance of almost always causing you to be dazed from the landing.
Also present in the game is the Topple status, which knocks the victim off their feet, and makes them completely unable to act or avoid attacks. It's essential to defeating some early bosses that can't be hurt while standing on their feet, and also turns into a bit of a Game Breaker later on, as topple inducing attacks can potentially be chained together to the point where the enemy can never get up until they're dead.
Specific chips like Air Shot in the Mega Man Battle Network series have this property attached to them and are handy for getting your opponents into the appropriate range for followup attacks. They can also be used on the otherwise harmless Rock Cube chip to send it flying into a target, which causes an excellent amount of damage early on.
The Dragonslayer Greatbow from Dark Souls deal tremendous knockback, even when blocked. This is exactly the reason why the weapon is so feared: the damage isn't that great unless you stat for it, but in several maps, getting hit by just one can spell an early doom by getting knocked back into a Bottomless Pit. You get to know this firsthand by having two snipers with said Greatbow sniping you from high atop a perch while you traverse a fenceless buttress. The archer also gets a little knockback from firing it, something that no other weapons do.
In Live A Live, there are certain skills that cause the targets to be pushed back a square or two, negating any charging skills they might have been using. While supremely annoying while trying to pull off some of your most powerful attacks, it can be used to your advantage by constantly delaying the enemy's most devastating skills.
In Tales of Symphonia and Tales of Vesperia, certain characters can have a special trait called "Glory" that prevents them from being knocked back. This was actually dangerous against some enemies, since characters with Glory would take multiple powerful hits when normally they'd only take one hit and be knocked away.
As mentioned, Rocket Jumping is a common technique exploiting the blasts from explosive weapons.
Golden Eye 1997 and Perfect Dark have a knock back for the player if they get shot. This also stops the player from shooting for a brief second. Combine this with several enemy soldiers and you're bound to lose more than half your health while unable to to fire back. Luckily, the enemy AI is programmed to stop firing for a moment and then resume.
Perfect Dark Zero also has it, making enemies that duel-wield machine pistols especially dangerous, with the possibility of stunlock.
The Medal of Honor games also have hit-stun. If an enemy catches you off-guard at close range with an automatic weapon on Hard difficulty, you may be stunlocked. Conversely, due to the use of Hit Scan, the knockback doesn't affect the enemy's aim, so they can continue shooting at you while apparently flinching. The snipers in Allied Assault not only deal the most damage and knockback of all mooks, but they also fire at a higher rate than the rifle infantrymen.
In Team Fortress 2 regular attacks have an amount of knockback generally proportional to damage and only something like the Heavy's minigun does enough damage for this knockback to impede movement instead of just messing with aim. There are some special cases which do much more: explosives, the Scout's Force-A-Nature, sentry guns (which can be even harder to deal with than its damage, especially since the default Ubercharge does not protect against knockback), melee Critical Hits, and the Pyro's airblast (which does nothing but knockback). Probably the most bizarre thing is that damage over time (fire, bleeding) causes upward knockback for the sake of messing with the user's aim. The Soldier's Mantreads and the Quick-Fix's Ubercharge reduce knockback by 75% and 100% respectively (though the Mantreads do not protect against airblasts).
Gears of War 2 and 3 implement a "stopping power" system where being shot slows the player's movement toward the shooter. This was added to prevent players from charging through a hail of machine gun fire for a close-quarters execution with a shotgun. In addition, smoke grenades in 3 (and post-patch 2) cause a flinch effect, while in 1 and pre-patch 2 cause full-on knockback, though they deal no actual damage in either case.
In P.N.03 the amount of knockback varies with the amount of damage inflicted by an enemy attack, with the strongest attacks blowing Vanessa clear across the room. In some cases, Vanessa mysteriously is knocked forward.
While Warcraft III doesn't feature knockback, the trope's omnipresence is such that it's a very rare (custom) map that doesn't have this mechanism (such as Defense Of The Ancients and its variants).
Dawn of War has knockback for artillery and some units. Justified for some (Super Strength, Psychic Powers, etc), but it does get a bit ridiculous when the Kroot (lanky hollow-boned bird-men) are upgraded to knockback units such as seven-foot-tall Power ArmoredSpace Marines with the same ease as ordinary Guardsmen and Gretchin. Also a fallen unit ordered to move will do so while playing their "get up" animation, so they end up gliding majestically along the ground before getting up.
Myth 1 and 2 have a flinch mechanic that is fairly central to gameplay as it allows certain rock-paper-scissors balancing. For example, the fast but unarmored Berserks can often kill heavily armored Warriors by whaling on them fast enough that the Warrior can't get a swing in from all the flinching. However, the same Berserks have a tough time against archers, as being hit causes the Berserk to stop running while he flinches—making him an easier target. Those heavily-armored Warriors are less likely to take damage from arrows, and still less likely to take enough to flinch.
Hoshigami Ruining Blue Earth has an entire game mechanic centered around knocking enemies into a chain of allies to incur massive damage and have a chance at stealing an item, but unfortunately setting up such a chain leaves your party very vulnerable so it's only useful for eliminating the last enemy on a map.
Dwarf Fortress has knockback as a possible effect of blunt attacks, launching the enemy a short distance calculated according to a staggering number of different variables. In previous versions this was insanely but hilariously overpowered, with even fairly unremarkable warriors able to launch opponents six or seven tiles. The recent combat mechanics overhaul makes knockback possible with all weapons, now that slashing or piercing attacks are re-rolled as bludgeoning ones if they fail to overcome the target's armour check, but for better or worse it also severely nerfed it.
Hack-and-slash Die By The Sword has a knockback system calculated by its complex physics engine, involving the strength of the swing (which is itself determined by character movement speed and mouse swing speed) and the relative sizes of the both characters (the larger Orcs will knock the smaller Kobolds around with even minimal mouse movement). Useful when knocking opponents into environmental hazards like spinning blades, bottomless pits, or lava.
Both character's weapons also get knocked back in a successful block, which directly affects their position for subsequent moves.
The knockback is explicitly exploited in the "Ogre Hockey" arena of the expansion pack, where the whole point is to knock the "ball" character into the opposing team's goal.
Tecmo's Captain Tsubasa, extraordinary strong shot and tackle techniques include a knockback effect that sends weaker oppornents trying to intercept the user across the field in an exaggerated fashion.
Despite the utter ubiquity of this phenomenon in video games, the actual Trope Namer for it is not a video game. The term "knockback" was first used to describe this effect in a game by the creators of Champions and the Hero System. When video games came along, the term had become so widespread among tabletop gamers (having migrated from Champions to GURPS to Dungeons and Dragons) that it was natural to call it this.