The Princess is usually considered the most useful of the four playable characters in Super Mario Bros. 2. Thanks to her iconic ability to float for a couple of seconds, she completely trivializes all platforming. Funnily enough, the Manual declared Toad to be this, due to his higher speed and power, but his poor jumping actually made him not very well suited for beginners.
Furthermore, because Peach has invincibility frames during her slow vegetable-pluck animation, this ends up as an advantage instead of a detriment, especially in hectic boss fights. Peach has the most invincibility frames since her plucking animation takes the longest.
Luigi in Super Mario 64 DS. The game was made for Mario's abilities, and most definitely not with the exaggerated jumping skill of Luigi in mind. Since his backflip allows for infinite gliding, and the Vanish ability is usable from all ? blocks, you can use it to get all the stars in Hazy Maze Cave without going through the poisonous maze, get most of the stars in Rainbow Ride without tricky platforming, and completely skip having to ground pound the pillars in Shifting Sand Land.
Hell, Luigi in general is quite superior (as far as platformers are concerned). In a platforming series known for its technical jumps and obstacles, being more floaty, having greater control over your movements in the air, and being able to jump higher and farther than your redder counterpart goes a long way in curving the actual difficulty of the game in your favor.
New Super Luigi U takes this to new levels. First, Luigi retains his floaty jump, and the Mini Mushroom is still in the game, allowing for even higher jumps. Taking the Spin Jump into consideration, the end result is a whole lot of distance for not a lot of effort.
Another game breaker in New Super Luigi U is Nabbit. He has the same jumping ability has Luigi, can't use powerups, and is invulnerable to any thing that isn't a One-Hit Kill, plus a few other large enemies that knock him back. You may not be able to fly with squirrel and propeller suits, shoot fire or ice flowers, or slide with penguin suits, but when you're practically invincible, who needs them? And in order to play as him in single-player, all you need to do is hold down a certain buttonnote B on Wii Remote, ZL otherwise and then you can breeze through the game, ignoring almost every obstacle.
The Cape earned its game breaker status with flying colors. It not only allowed Mario to perform sustained flight (which, given a few minutes practice, allows you to bypass most levels by taking a running jump and hitting the left directional button every few seconds), but it also gives him a spin attack powerful enough to kill most enemies. Even more effective is when he is flying, it is the only instance where Mario does not lose his power if he gets hit by an enemy. It also allows you to fall much more slowly than you normally would, so you can control where you'll land. To top it all off, it also comes with a screen hitting ground shaking landing.
The Blue Yoshi (which lets you fly when he eats a Koopa shell of any color). You can find this variant in two ways: A) Hatch one in Star World 2 (the water stage) and feed him 5 enemies or 1 power-up to make him mature; or B) Use any breed of Yoshi and catch the pair of Magic Wings on the Cheese Bridge stage, which turns him into the blue variant. Once you have one, you can then bypass entire stages easily: Simply slurp up a Koopa, hold up and right, and wait. It's the easiest way to pass the hardest level in the game, the Special World's "Tubular" level. It's that useful.
Powerups in general are quite effective in Super Mario World. Whereas there are a finite number of Hammer Suits, P-Wings and Tanooki Suits in Super Mario Bros. 3 (and are a hassle to farm in remakes where they are infinite since you still have to play the levels in that World all the way back to the vendor), you can just backtrack and get another Blue Yoshi or Cape with much greater ease.
The Game Boy Advance version made this even more conveninent, by making Yoshis of a certain color available from any Eggs spawned from ?-Blocks (once fully grown in the Star World, of course), and also dependent on what power-up you currently have. Essentially, having the cape guarantees that any eggs spawned from ?-Blocks will consistently hatch a Blue Yoshi.
There are several opportunities to get tons of extra lives. By the time you finish the Forest of Illusion, you'll have maxed out your lives to 99 easily. Notable examples include:
The earliest example was in Donut Plains 1. A training area exists (that is accessible right beside the midway goal) where players can use the Cape (with sustained flight) to glide through a massive block of coins spread out across a long distance. Experienced players could hit the midway goal, go into the area and fly back and forth through the coins, racking up two or three lives in the span of a minute-and-a-half, then exit out to the level screen. Wash, rinse and repeat.
The Top Secret Area is a secret level accessed through the Donut Ghost House (right at the beginning of the level, fly up). The accessible level included full item pickups (mushroom/flower/cape), a Yoshi, and a single 1-up every time the level is accessed. This led to the player being able to grab extra lives whenever they wanted.
In the Forest of Illusion, a glitch can be exploited (float back and forth using the Cape between a set of three Wigglers) that would max out your lives and score in three minutes. The game can't even properly describe what happens when you start receiving 6 or more lives per successive hit (and resorts to illegible programming language to show it on the screen).
Another thing you can do in the Forest of Illusion is in the first stage of the world. Take a Starman from the changing block immediately after the halfway point, run like crazy through the rest of the level, and you can get up to 17 lives in under a minute.
There's also Vanilla Secret 2. The first half of the stage is filled with dozens of hopping Koopas, but directly after the mid-point is one of the silver P Switches. These switches turn all enemies into silver coins, which add up during collecting like successive stomps on enemies without landing. All you have to do is carry the P Switch over to where the Koopas start, stomp it, and haul plumber ass towards the right side of the stage. This method takes awhile to rack up the lives though....mostly because you get so many in that twenty seconds or so that the game needs a couple minutes to catch up.
Unlike the overpowering cape, the Super Leaf in Super Mario Bros. 3, which turns Mario into Raccoon Mario, only allowed him to fly for a few seconds, and its spin attack is much slower and much shorter in range. However, the Tanooki Suit, which is essentially an enhanced version of the Super Leaf, simply dominates over that and the other flying powerups for one simple reason: its statue mode. It renders you immobile and it only lasts a few seconds, but you can also slide under gaps that are too narrow for even small Mario if you're on a conveyor belt, as well as being able to kill nearly any enemy by statue-stomping them from above, including the otherwise-invulnerable Rotodisk.
The Hammer Suit from the same game has Hammer Bros-style hammers that go through structures and enemies and have hilariously high damage output; one hit will defeat Boom-Boom and any of the seven Koopalings, and six hammers will take down Bowser himself. Hammers are also capable of killing otherwise invincible enemies such as Fire Lotuses, Boos and even Thwomps. The only enemies they can't kill are the Munchers (tiny, black Piranha Plants) and Jelectro AKA Immortal Jellyfish. And that's only because, on a technical level, Munchers and Jelectro act as blocks.
Super Mario Advance breaks itself with the Giant Mooks. Every time you toss a big Shy Guy or Ninji to the ground, they spit out hearts every single time.
The 4th and final Advance game in the series (based on SMB3) can be quite effective if you have the e-Reader and the cards that go with the game. You can easily get many power ups and extra lives by swiping the same cards into the game over and over. And yes, you can even get the Cape from Super Mario World this way.
There's a card which gives you 100 extra lives every time you use it. Just one use will completely break the game's difficulty to zero.
New Super Mario Bros. has the Mini Mushroom. It shrinks Mario down to half his small form's size, and while it makes him a One-Hit-Point Wonder who can't even kill enemies without a ground pound, it makes him more floaty, gives you greater control over his movements in the air, lets you jump higher, further, faster, and makes you far harder to hit, in addition to being able to run across water. In short, it essentially trivializes all the platforming in the game; even most bosses are far easier once you get the timing of the ground pound down.note (Which is good, considering you need to beat two bosses in mini form to unlock two of the worlds.)
The game's own playthrough videos frequently abuse the Mini Mushroom power-up's inability to Goomba Stomp enemies with the standard jumps to ride Bullet Bills across entire levels for extra lives and profit.
The Mega Mushroom can be held as a secondary item in the bonus stage houses. Use it against Bowser in the final battle, and you just have to walk over him in the easiest final boss battle ever!
New Super Mario Bros. Wii gives us the Propeller Mushroom. It acts like a mega jump, it allows you to glide, and then you can fall on enemies at high speed to kill them. Basically, it's the power of flight all over again! In addition, having it guarantees getting a 1Up at the flag, unless you seriously botch it.
A similar item, called the Propeller Box, appears in Super Mario 3D Land. In addition to guaranteeing you the golden flag (and extra life) at the end of the level, finishing the level with it will give you another extra life. There are also several areas (particularly 2-3) where you can chain jumps together off flying Goombas to get even more lives.
3D Land also has the Statue Leaf. The normal Tanooki Suit is already rather useful because of how you can glide, but the statue form lets you kill/stop ANYTHING you fall on/in the path of. Thwomps get smashed to pieces, flames do nothing, enemies ignore you or die in one hit and even giant Pillars just stop dead on contact.
If you have either of the leaves, you can literally skip some of the boss fights by simply gliding to the button that defeats the boss.
The most powerful leaf in the game however, has to be the Invincibility Leaf and subsequent White Tanooki Mario. It's basically the game's regular Tanooki form but Nigh Invulnerable to anything that's not a One-Hit Kill and able to kill roughly any regular enemy on contact with no time limit (though it will revert to regular Tanooki suit once the stage is cleared). This is justified though, since you only receive the leaf if you lose five lives on a given level, making it the game's easy mode. It appeared in New Super Mario Bros. 2 (as White Raccoon Mario) and Super Mario 3D World, with its effectiveness in the former being taken Up to Eleven for five reasons: 1) it has the same flight abilities as 2's basic Raccoon Suit but the p-meter fills faster while running, 2) it can Walk on Water, 3) it works just as well on bosses; though it still needs to hit Koopalings three times, it one-shots Bowser's first form, 4) it can be used in Coin Rush mode without having to die at all and 5) the block that gives you the power-up won't disappear once the level is finished or the game is beaten.
The Super Bell in Super Mario 3D World is already being called this. The ability to climb up walls is immensely useful and can easily save players who accidentally fell down a bottomless pit, and a close-range attack is always a good thing to have. This is somewhat balanced by it having a bit of a learning curve, as it's rather easy to kill yourself by accidentally dive bombing off the stage.
However, it is topped later by the Lucky Bell. Similar to the Statue Leaf from 3D Land, this power up has the same function has the Super Bell, cat powers and all. However, it ups the ante considerably because when you ground pound, you become invincible. Enemies can run into you and they will die upon contact. Bullies giving you trouble because you have to knock them off? Let them run into you. Oh, was it mentioned that you get free coins for simply ground pounding? It depends on the height that you ground pound at, so the higher up you are before you ground pound, the more coins you get. And you first receive it in one of the tallest, most vertically oriented levels in the game... the Lucky Bell is one of the strongest power ups in the game, perhaps one of the strongest in the whole series.
In New Super Mario Bros. 2, the Gold Flower is this. Turns Mario into gold, doubles his coin haul from pretty much everything that gives out coins and can kill nearly all enemies in one hit (and hit a whole screen full at once). Bowser's first form? Down in one hit. Dry Bowser? Down in one hit. Multiple Reznors? Down in one hit. Sure it goes away once you beat a level with it, but you can bring them into any level in the game...
In Super Paper Mario, Bowser seems very powerful at first, given the fact that he is twice as powerful as any other character and is capable of killing enemies at range with his fire breath...until you realize he is slow, a big target, and only capable of firing his Breath Weapon from the ground. Reasonably balanced enough, but by combining Bowser with the Pixl Carrie, who increases movement speed (and note well that Carrie's speed is the same for all characters), we have a Lightning Bruiser on our hands who gives us little reason to use anyone else unless the platforming requires it, and this is before we even factor in the thing that truly makes Carrie Bowser great: Carrie is a platform under the character's feet, which means whoever uses Carrie is treated as on the ground even while jumping. To reiterate, Bowser is capable of firing his Breath Weapon only while he is on the ground. The game was very clearly not designed around the possibility of Bowser jumping and killing enemies at range, and it allows Bowser to kill nearly any enemy before they can even get close. The fact that Carrie allows Bowser to jump on most examples of The Spiny and not take damage is just the icing on the cake.
Luigi as well, despite his late entrance to being playable. He has the speed of Mario, even greater agility than the other characters, and his spring jump does double damage from below, while none of the other characters can attack from below at all. Note that charging the spring jump only increases its height, it will do double damage no matter how little you charge it.
Similar to Bowser, Peach becomes much more powerful when using Carrie. She has a move that grants her complete invulnerability, but as with Bowser's flame breath, she is immobile using it and must be grounded. Again, factor in that Carrie makes Peach grounded all the time and faster means you can easily move around and attack enemies while remaining completely impenetrable. Many a challenge becomes very easy abusing this.
While the Pixl Dottie is fairly mediocre in the main game, in the Pit of 100 Trials, she doesn't so much break the game as destroy it. In a Multi-Mook Melee, the ability to keep enemies from noticing you're there at all is more than slightly overpowering.
The first Mario & Luigi game (Superstar Saga) had a series of badges called Shroom Badges (Shroom Badge, Shroom Badge A, Shroom Badge AA) that increased your attack proportional to the number of mushrooms you were carrying. Ostensibly, this was supposed to have the penalty where healing yourself costs you attack, but it is both cheap and easy to carry almost 99 of all FOUR kinds of mushrooms and to heal only using Nuts. Since carrying around 30 of each kind of mushroom was enough of a game breaker, just imagine what 396 mushrooms must be like.
Funny thing is with the Shroom Badges is that the damage increase also affects First Strikes. With enough mushrooms, you can instantly kill a lot of enemies without even starting the battle.
There's also the Bonus Ring, which doubles your experience if you manage to not get hurt in battle. It's available as soon as Starbeans Cafe opens (You need to blend two different drinks for it). Since it's possible to avoid every enemy attack in the game, you can level up high enough to defeat the final boss by the time you're in the Beanstar Fetch Quest if you're good enough.
In the DS sequel, Partners in Time, there is the inexpensive Practice Badge right from the start, which bless the bearer(s) with infinite use of attack items at the cost of attacking power. Maybe they're weaker, but with a little practice you'll be able to spam quite high damage using Pocket Chomps, Clone Flowers or Red Shells, and not worry about buying any, saving all your money on healing and buff items. You probably won't even have to buy a single of these weapons if you grind enough, and as long as there's at least one available in your inventory, you'll be able to sell them for quite a price (more if you max out your characters' mustaches).
Heck, red shells in general are quite useful in this game. You can keep them going forever as long as you don't miss, which surprisingly isn't that hard thanks to their speed capping out early and at a manageable speed. Although for good reason, red shells aren't available until after Thwomp Volcano.
There's also the Ulti-Free Badge, which makes it so that you don't use up Bros. Items, but you need 90 beans in order to get it, which means that it usually can't be obtained before Thwomp Volcano, later in the game.
In Thwomp Volcano you can get a potentially unlimited supply of beans through the mini-game. Despite the fact that each time you play costs 100 coins, combine that with some easy ways to get coins really quickly in that same area and, with enough grinding, you can get badges for everyone.
For Bowser's Inside Story: The Broggy Bonker could count as this for Bowser. It's his ultimate attack which does ludicrous amounts of damage as well as being quite easy to pull off, which coupled with the Economy Ring (reduces SP usage by half) makes it incredibly spammable.
Don't forget about what happens when Bowser reaches level 40, he receives the Intruder Fangs which allow him TWO actions per turn! Combine this with the King's Shell which is his best defensive armor, and raises his punch's power by 30%, then use moves like Broggy Bonker twice in a row to see how Game Breaking Bowser can be.
There's the Magic Window ability which allows Mario and Luigi to summon endless clones of themselves as long as you pushed the correct buttons at the right time. If you were quick enough, most enemies and bosses could be defeated by this single ability alone.
Then there is the Mighty Meteor special attack; by the time you get this, you can stock up on the best healing items in the game as after completing said move successfully, an item pops out based on how strong the enemy was. Use this move in the Airway section to get Star Candies.
Mario & Luigi: Dream Team has the Birthday equips, which have unimpressive stats under normal circumstances, but if you play on whatever day you registered as your birthday on the 3DS, their stats quadruple, making them as strong as the endgame equipment, only they're obtainable much earlier and lack the drawbacks some of said equipment possesses (Such as having a chance to break upon being used or damaging you along with your enemies). The 3DS allows games that use the date to set an Obvious Rule Patch penalty for changing the clock settings, but Dream Team doesn't bother, and if you want to avoid taking the penalty on your other games that do, you can just change your birthday.
There is also a certain badge effect (gained by using the Gold and Miracle badges together) that freezes time and stops enemy movement for about three turns. And the badge slots used to activate it can be filled by fighting weaker enemies beforehand and doing 'excellent' attacks. So you can literally beat any boss in the game by getting this badge combo, grinding on a bunch of weaker enemies to fill the slots and then freezing time immediately to stop it attacking before blasting it with every Bros Attack possible. Did I mention how the DOB equips can be stacked on top of this effect, and how the items affect Bros Attack power? And that you can use this effect up to four times in a row? So you've got 400% attack power, no way for the enemy to fight back and attacks that already do about 500 damage per hit. It can let you beat the final boss in under a minute!
Interestingly, it also completely stops bosses using their special abilities to defend themselves or anything, so you can just use it on the Bonus Boss, then not have to worry about him ducking into the Clown Car to block your attacks. The final boss can't protect his weakpoint if you use this badge either. And you can even use it during Pi'illodium's self destruct count down to STOP THE TIMER. This can make the battle very, very easy at that point, since the badge can be used to do this repeatedly in a row.
There are others too, such as...
Boost Wear. Your badge meter goes up every time you're hit by an enemy. Sound not great? Well try using it with time freezing abilities. Or worse still, in the Antasma/Antasma X fight, where his attacks like the bat charge and the buzzsaw gauntlet dream world chase hit you tens of times in seconds! Seriously, you can fill up your badge meter in just one or two battles in the Battle Ring with this. There's also the Rally Belt, which boosts your POW whenever this happens, sort of like how Big Massif attacks in Dreamy Wakeport. The latter is really hard to get, but potentially available before the halfway mark.
The Challenge Equipment which becomes stronger the more challenges you complete, and eventually becomes some of the strongest, if not the strongest equipment in the entire game if you do all of the challenges in the game. This is due to the fact that finishing the list completely gets you the Duplex Crown mentioned below.
The Duplex Crown. See the Intruder Fangs in the last game? Just as useful this time around, being able to move twice in a single turn. In the Battle Ring, this basically doubles the turn limit.
The Golden Equipment which has stats that are based on your overall coin amount, meaning the more money you save, the stronger it is. This eventually can become so strong that at max power it's only second to the Challenge Equipment seen above. This becomes extremely easy when you realize that you don't have to shop for items and weapons as much as you think considering that a lot of ones will probably be dropped from enemies along the way, allowing you to save up money easily, especially with the Coin Gloves DX equipped.
Bottomless Gloves. Infinite items (aka your healing items never run out). In the Battle Ring, this completely annihilates much of the difficulty.
Coin Gloves DX and Gift Gloves DX. Using one of these on each of your brothers respectively means that both your chances of getting items (including rare ones) and your coin amount from enemies at the end of battle are significantly increased. The Coin Gloves DX are found by beating Madame Brioche's Luiginary Ball event which isn't too tough (at least compared to the other events in her arena) and the Gift Gloves DX are the rare drop from Bandits which are easy to beat, and come in groups, which make finding them pretty easy.
Strike Badge. Does a fixed amount of damage (that doesn't use up your turn) and can be done until your badge stocks run out. One possible effect with it is to do 80 damage at any time. There's a boss which has be defeated quickly (in three turns) and that only has about 280 health. Difficulty kind of evaporates then.
Silver + Miracle Badge combo. Reverts status to last turn (which can act as a full heal on demand), restores any BP used or items used from the inventory, is very easy to charge up, and can give you back the Bros Attacks Bowser Jr steals so you can use them twice in a row.
To add to this... badge effects don't use up a turn. You can use infinite amounts in one turn. And what happens if you use this effect? The badge slots you used come back! So just set the Gold/Miracle Badge, a Guard Shield Badge and the POW Up effect up before you start a battle. Then use them all. Once this is done... use the rewind effect and voila! All three used badge slots are full again, giving you another round of time freezing/POW boosting/impenetrable shields! Finally, the Miracle/Silver badge combo charges super quickly in battle, so you can theoretically do this up to five or even ten times in one fight if you're lucky.
Badge Charge Meter Badge Effects. Can charge up OTHER badges immensely in a very short amount of time. Like, fill whole meter in a turn type quickness.
The Casual Bros. Bonus power which halves your Bro Point (this games version of Magic Points) consumption. There's an accessory called the Bros. Ring which does the same thing, and can stack on top of this effect as well which makes it so that one brother can literally use his Bros/Luiginary attacks for a quarter of the normal amount.
The Angel Bangle, which restores 20 HP and 10 BP per turn. If you then use Casual Bros... no Bros/Luiginary Attacks AT ALL use more than 10 BP per turn. Cue infinite special attacks used non stop for the rest of the battle.
The Star Boots, which make any jump attack or special boot based attack recover health after you damage an enemy. Combined with the Angel Bangle, you'll probably never have to worry about health again for the most part.
Guard Badges too. Shield that nullifies all damage until each bro has been hit six times? On command? Yeah, that's more than a little overpowering. Their equippable variant of the Guard Shell is similarly useful, nullifying the same number of hits and also refreshing the barrier if a Bro is KO'd then revived.
The Master Gloves. If you get an Excellent on a Bros. Attack or Luiginary Attack, your BP is refunded. Translation? You can spam away with the strongest attacks in the game if you can use them perfectly. Syrup Jars? Who needs them any more?
The Slingsniper, despite not being the last Bros. Attack you get, has a special property to it that can make it way stronger then any of the other ones in the game if it's used properly. If you're fighting a large enemy, a star indicator will appear on them, and having Luigi score a direct hit on the star will cause the already strong attack to deal a critical hit for even more damage.
This game has possibly one of the most useful accessories in the entire series if not the single most useful one, period. If you go to the beginning of the last dungeon Neo Bowser Castle and fight a Flaming Antasminion (a little purple Antasma robot with wings that spits fire), you have a 1% chance of them dropping their rare item (though this can be boosted by the aformentioned Gift Gloves DX), the Farmer Boots. To make up for the fact that there are considerably fewer beans in this game than previous titles, these boots more than make up for it in spades. If someone equipped with these boots jumps on or uses a boot based special attack on an enemy to defeat it, the enemy has a good chance of dropping beans instead of coins. This becomes extremely useful when you realize that you can get two pairs of Farmer Boots (one for each brother), go back to early parts of the game with weak enemies that don't have spikes (who are immune to jump attacks), jump on them for a pre-emptive boot attack which at your current level should be an instant victory and literally reap what you sow when the enemies each drop beans that you can use increase your stats including your stache (which is your luck stat used to determine critical hits) that normally doesn't level up unless you use your level bonus when you level up on it to insane levels. The game and all of its difficulty, including the battle arena will literally fall apart when you realize that you can do this in earlier dream dungeons where enemies attack in swarms which means you can literally get a dozen or more beans per fight.
In Super Mario RPG, Peach is practically a game breaker by herself, and that's just the start of it. She's the only character possessing full party heal and resurrection spells, making any party with her extremely hard to kill as long as she's alive. This becomes doubly beffective once you get the Lazy Shell armor, which in turn for weakening wearer's attack powers highly buffs their defense. On Peach, this results in a minimal reduction to her healing abilities in exchange for making her almost impossible to kill, turning her into a White Magician Girl who can heal the entire party at once — status effects and all — for 4 MP, revive party members to (almost) full health (if you get a Timed Hit) for only TWO, and is herself immune to pretty much everything except HP to 1 and One-Hit Kill moves. Then give her the Quartz Charm you receive for beating Culex to significantly raise her stats, as well as making her immune to pretty much every status condition in the book for true Game Breaking ability.
By the way, she tanks relatively well once she starts gaining levels, even without the Lazy Shell, and gets some pretty awesome weapons, so not only can she heal, she can bust out some massive damage herself. It's not as good as Bowser, Mario or Geno, but good enough to get her by without Psycho Bomb.
By the same token, Mario equipped with the Super Suit is an unstoppable tank. It has virtually the same effects as the Lazy Shell Armor but with better stats (and no attack penalty). The Super Suit could be obtained as soon as you reached Monstro Town if you were skilled at timing your Super Jump attacks. You could practically take Mario into any battle alone (letting the other two party members die or otherwise make them block), and to further pile on the overkill, equip him with the Lazy Shell weapon and Attack Scarf. Once you have these three items no boss in the game can stand up to you. This is balanced out by the fact that 100 Super Jumps is absurdly difficult to pull off, and the armor itself can't be obtained until the game is 3/4th over.
Any player who could master timed hits became a killer machine with Geno. His Geno Whirl attack timed hit does 9999 damage each time for a small amount of flower points. No, seriously it does that much damage when timed correctly, making any enemy not immune to it (including one of the endgame bosses) a joke.
The Safety Ring makes an individual into a game breaker in and of itself. It protects against all magic damage (though some abilities are considered physical), all status effects, and instant death. And it's relatively easy to find.
In Paper Mario, equip Mario with the Power Bounce badge (which lets you jump on an enemy repeatedly, provided that you nail the Action Commands) and the Charge badge. The Charge ability ups Mario's attack power and can be stacked. Thus, all you have to do is keep charging Mario for about 4 turns, then unleash a Power Bounce. Get the timing right, and you can do 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and then boom. You just did 55 damage, in a game where the most powerful boss has 100 HP. The fact that one of Mario's partners can pull off the same exact strategy helps.
The Thousand Year Door takes this up a notch: Mario can do the same thing as the first game, and has a Yoshi partner who can also charge and pull off a multi-hit attack - but said partner has another multi-hit attack that hits ALL enemies on or near the ground. With enough Charge P badges, even most of the more dangerous enemies in the game can be reduced to a two-turn victory.
If you're particularly good at keeping your Power Bounces going you can take down any enemy, bosses included, just by bouncing forever. The sequel capped the amount of times you could bounce.
Paper Mario: The Thousand-Year Door has a good number too, generally centered around turning Mario into a Glass Cannon. The craziest is the "Danger Mario" setup focused around the Power Rush badge. It adds two attack when Mario has 5 HP or less, it stacks, and you can buy as many as you want. Add in the stackable badges that make attacks sometimes miss, drop Mario's max HP to 5, and you're permanently superpowered AND nigh-untouchable. Works even better if you add in the Spike Shield and Ice Power badges which make Mario able to jump on enemies safely, as unlike his hammer attacks, Mario's jump attacks usually hit multiple times; Power Bounce with the Danger Mario setup equals a brutal and crushing defeat for all of your enemies. Finally, add a few Life Shrooms in case Mario does get hit and die, and the rest of the game becomes a breeze. This is alleviated somewhat by the fact that you can only drop Mario's max HP to 5 by visiting Chet Rippo, whose shop becomes accessible late in the game, but it's nonetheless useful as hell for the rest of the game, as well as the Pit of 100 Trials.
With the Spike Shield and Jumpman badges Mario can completely eliminate all need for the hammer and get a decent attack boost on the jump which can now be used on (almost) all enemies. Add in one of the two or three items that allows one to hit flaming enemies, two or three Power Plus badges, and a couple of P-Up D-Downs and Mario is a killing machine that can do damage above and beyond that possible in the original game's method with just a charge or two combined with Power Jump. Even better, so long as Mario has about 15 HP just in case it doesn't matter how bad his defense is — The Thousand Year Door introduced a very easily exploitable ability to have one of your partners serve as an impenetrable Stone Wall. And one of those partners has this move called Rally Wink that will give your super killing machine Mario another turn each time it's used.
The only problem with this is that Mario can't hit enemies on the ceiling, although there are several partners who can, and that usually knocks them off.
Get a lot of Super Appeal badges (About 10 should do it) from the Pianta Arcade, equip them, then Appeal as Mario. Your star meter is completely filled.
Spin Off Platformers
Bunny Mario from Super Mario Land 2: 6 Golden Coins. Bunny Mario is essentially taking Princess Peach's already game breaking float ability from Mario 2, and grant players the ability to pretty much stay airborne as long as they please, provided they tap (not hold) the jump button. You are also granted a much higher jump and much easier air control. The advantages of the bunny power more than make up for the slight disadvantage of not being able to spin jump. You'll never worry about platforming in the game ever again.
Collectable items in Yoshi's Island. Not really any particular ones, just any you can store in the inventory. Sure they're blocked from being used in boss battles, but being able to breathe fire/freeze enemies/shoot bullet-like seeds at any point in the game? Effective to the point you can often just blast the spike pits to pieces and stroll through. Getting 20+ stars is basically an instant max health refill, and the items to change enemies to clouds or stars make tough areas a breeze, as does the ability to turn all red coins red and be able to tell them apart from the normal ones. Naturally, they were completely removed in Yoshi's Island DS, forcing those seeking 100% Completion to earn their 30 stars the hard way (especially in 1-Secret, which has exactly 20 stars in the entire level).
The Jet Hat from Wario Land breaks the game wide open and then breaks it even wider out of spite. It allows for a smooth 8 second sustained flight and then glides downward until it touches land. Due to a quirk in the programming, though, you could at anytime during flight press B to stop flying, and then press B to start flying once more. With practice it's possible to essentially fly forever, and clear entire levels without even touching the ground. For icing on the cake, the jet hat is also a fairly common item, boosts your jumping height, and makes you run faster.
Mario Party 3 had the Reverse Mushroom, an item that, when used, forces the target to move backwards on their next roll. The conveninence comes from the fact that going backwards is actually quite handy more often than not: it can be used on yourself, it can send people off into undesired areas, it allows the "afflicted" person to go in any direction at most junctions — and could thus "backtrack" to the Star Space you might have missed or have been unlucky enough to be at another area or path when it respawned, it can also let you go to areas that are normally impossible to enter without a Skeleton Key — which tend to have Chance Spaces and Item Spaces littered there. Oh, and a random Bowser event can inflict everyone with this status. Simply put, it was not a coincidence that it was one of the very few items did not ever reappear in any future titles (that wasn't tied to the gameplay that is), even in other forms.