One of Colette's level 2 techs in Tales of Symphonia, Para Ball, only uses 14 TP and is stronger than most level 3 techs.
Don't forget its near-guaranteed hit stun (and ability to stop all spellcasting by itself). She's an absolute monster in the arena for that reason.
Also, once you get the hang of spell canceling, you can perform an essentially infinite combo with Colette if you have an angel tech set to B. Attack twice (non-directional), then quickly press B, then X, then attack twice again, cast and cancel, repeat. This works with any enemy that can stagger, and since the spell doesn't activate, it consumes no TP. Needless to say, it makes the arena a piece of cake.
Sheena can do this, too.
As can any character with access to any sort of spell. That's all of them except Lloyd and Presea, though Genis won't be making much use of it because of his already slow attack speed and strength. However, it's very possible for White Mage Raine to solo the Bonus Boss Abyssion using this tactic, combined with the fact that for some characters, it's ridiculously easy to get immunity to the elements. See here. They tried to fix it in the PS2Updated Re-release, but it still works if you have a spell you've used 999 times.
Colette's Toss Hammer is a Level 1 Tech that randomly activates instead of Pow Hammer (fairly often) after using the latter 200 times. Easier than it sounds; Pow Hammer is gotten at a very low level, and through the course of battle you'll end up using skills a lot. Alright, so what's so bad about Toss Hammer? The poison damage it does is fast and hits hard, being percentage based- to the point of being able to take out 240,000 hp within a minute and a half. Right here. You can see the HP tick down when he uses a Magic Lens at 01:31. Oh yes, this Colette's at level 6.
It gets broken even further. Once Pow Hammer has been used 200 times, her Pow Pow Hammer and Hammer Rain skills will randomly include at least one Toss Hammer. If the tech glitch has been used to get Hammer Rain alongside Para Ball...
Lloyd's Devil's Arm quickly becomes infinitely more powerful then any weapon in the game (doing more then 10 times his next most powerful), because the Devil's arm increases when the character makes a kill (even if they haven't found them yet), Lloyd, being the main character, is in the party for all but two short sections and gets the lion's share of kills over the game (and kill count can be carried over for New Game+).
Tales of Vesperia features the exact same premise. Once the player unlocks the true form of the Fell Arms, granted that pretty much everyone will play as Yuri, the Blazor Edge Abyssion will have somewhere in the range of 2500-3000 more attack power than any other weapon in the game for Yuri.
One of Genis's possible EX-Skills is Randomizer (combine Tough and Rhythm). This skill makes his spell-casting times random; every once in a while, the spell will cast instantly. If you control Genis, you can alternate between the B and X buttons (which will repeatedly start and cancel a spell) until the spell casts instantly; this oftentimes makes the spell cast very quickly, even for high level spells, and you don't have to worry about being interrupted in the middle of spellcasting, making the tactic a quick way to bring down even the toughest bosses with a near-constant onslaught of powerful magic.
You can also do this with Raine's EX-Skill Quick Spell (Neutralizer, Spell Save, and Happiness), which causes a spell to cast instantly about 10% of the time.
Sheena has the Hard Hit EX skill, which increases the hitstun caused by her attacks. She also has the Force Seal spell, which also increases hitstun (and stacks with Hard Hit). Finally, her Serpent Seal Pinion has extremely low recovery, to the point that if you have Hard Hit and either cast Force Seal or attack from behind, the enemy's hitstun lasts longer than the recovery from SSP, allowing you to repeat your melee combo > SSP over and over again to keep the enemy perpetually stunned. With this strategy, Sheena can easily solo some bosses like Seles without letting them get off a single attack.
The sequel also has Marta, who has Speed Cast 1, 2, and 3. Stack all three with some Speed Cast equipment, and she can cast virtually any spell near instantly. Add in one piece of equipment she can get at the start of the final chapter which makes all Artes, spells included, consume only 1 TP (when you're likely to have hit the 999 cap on max TP by this point on a New Game+), and she can single-handedly create an infinite combo by spamming Photon until the enemy keels over.
And don't forget Emil, also from the sequel. With the skills Accelerate (which he could only get from two weapons: his best and a weapon that can be forged as early as chapter three) Glacies, Ability Plus, and Ability Plus 2, he was capable of infinitely comboing anything by simply using Blade Fury (which, due to Glacies has an extra stunning hit at the end) twice, then using any ground based Arcane arte (Sword Rain Alpha and Light Spear Cannon are the most popular), then just repeating the process by using Blade Fury twice again.
And if that seemed too complex, by simply equipping one of the Accelerate weapons, with no other skills, Emil can do an infinite combo with his physical attacks.
Guy from Tales of the Abyss. The game uses a strange combo system for attacks, where using a level 2 or above elemental spell or arte produces a Field of Fonons that was about 25-50% complete. In order to use them, you kept using those attacks until it was 100% formed, and then anybody standing inside it could use an appropriate spell that would absorb the Fonons and make a newer, better spell. Character skills and spells and techniques were customizable with Chambers, one of which (Sunlight) allowed you to use a Field of Fonons before it was complete. Guy had an Arcane arte that created an incomplete Wind Field and also tossed the enemy in to the air. You could immediately combo it in to a Base technique (Void Tempest) which would immediately use the newly made Wind Field to become Dragon Tempest, hitting the enemy before they managed to hit the ground, stunning them AGAIN, which meant you could start the combo up again. This is Guy in action taking on the Bonus Boss starting at one health, never healing, and winning using this tactic.
To elaborate on the combo system: normally it goes normal attack to either a Base arte or Arcane arte, but Base can chain to Arcane. Arcane can't chain to Base though; there's a noticeable delay in comboing, which will kill the combo- unless you get the the skill Super Chain. However, a Fo F skill such as Dragon Tempest can be chained FROM anything and can chain INTO anything... so yeah, there's an infinite combo for you. Let's also throw in the fact that Guy is usually the character to end up with the most speed, and all his techs are fairly rapid already.
Also from Tales of the Abyss is Anise's Ant Lion Man doll. It restores her HP and TP by 8% every 2 seconds or so. On paper, this doesn't look like much, but in practice this is an insane amount of healing. Imagine a mage who never runs out of TP, and who is also a Mighty Glacier that can only die to a One-Hit Kill.
Even more disgusting is the Jewel of Lorelei, which you get automatically through story events, and gives the same benefits to Luke. So you can have two effectively unkillable fighters on the team, one of whom is a combo fiend and frontline fighter. It's a shame that, except for a glitch only found in the original Japanese version, you have to give it up.
Tales of Vesperia includes a marginally weaker version of this in the Final Symbol. It's remarkably easy to gain seven of them.
By using the map glitch, you can get Luke a fancy sword as soon as you can explore the world map. By why stop there? If you saved up enough Gald and carried it over to your new game, you can go to Keterberg and buy the party Mythril weapons and armor, and stock up on gels and bottles. Now you can go outside and fight all the high level monsters (the party will still die a lot, but you stand a better chance with the weapons and armor you just bought). You can get from level ten to level thirty in about an hour (it's even better if you started with an EX Px 2 or EX Px 10).
Jade has his fonic powers sealed due to plot reasons, and he takes a while to build back up and unlock his various spells. If you give him a Capacity Core that boosts the Enhancement stat, he will eventually learn the AD Skill "Glory". Glory makes a character completely immune to stagger/flinching. Jade will then be able wreak havoc from afar, tossing out spells left and right with no fear of his incantations being interrupted. Tear can do something similar. Her offensive spell selection is much more limited, but Holy Lance is a very good spell.
Rita in Tales of Vesperia. Get the Spell End and OVL Boost 2 skills, equip the Risky Ring, shortcut Tidal Wave to the A button, set all of your other characters to taunt. Go into battle, launch the enemies into the air with a single level Overlimit, mash A. Have fun. And don't forget to use another overlimit when the overlimit ends. Alternatively, you can also use the Minimum Damage skill along with it to farm Grade off of enemies like no one's business.
Wonder trinket allows you to fit in even more tidal waves. Violent Pain is used the same way on single foes, to maintain permanent overlimit.
Estelle is the real game breaker. Due to an unintended oversight (which was fixed in the updated PS3 release), the spell Force Field makes the target invincible for a few seconds, but with the Eternal Support skill, there's a chance it'll last for the ENTIRE BATTLE. Put the skill on, spam Force Field until it sticks, and you can't lose.
You have to work a bit to get Yuri's infinite combo going, it requires the enemy to be stunned (with the spinning stars) early on so they can't break out of it, and it only works against solo enemies, but once you get the hang of it and remember to reset the fallen enemy with his free-run slash, Yuri becomes impossible to stop, especially against human enemies. There are videos of Alexei,Flynn,Duke, and Kratos all being brought to their knees by an infinitely-comboing Yuri.
The PS3 version makes Yuri even more broken with the addition of his Vesperia No. 2 weapon, which gives him a second Mystic Arte, Tenshou Kouyokuken. With the Combination skills, Yuri can build up a 100x multiplier to be applied to the next attack that hits the enemy. Tenshou Kouyokuken is one of the strongest single-hit attacks in the game, probably second only to Indignation. Throw in the Barbatos Ring, which gives an incredible stat boost at the cost of not being able to use items, and painful destruction ensues - imagine One Hit KOingevery boss in the game.
It's possible to infinitely time stop anything in the game without much effort, completely removing any difficulty whatsoever. All one needs to do is get Raven's Stop Flow spell(Stops time for 5 seconds with a long cast time and high TP cost), equip him with the Risky Ring(Makes all Artes cost 1 TP), activate Overlimit 1 for instant cast time, and beat anything on the screen to death. With minor use of limit bottles, it's possible to maintain this technique for essentially forever.
While not exactly useful against bosses, assigning Sylph and Arche's weaker spells to your hotkeys basically ensures an instant win against the incredibly powerful monsters in Shadow's cave. Being able to cast high level spells much faster than your characters can is not as useful as you'd think when the other guy is constantly knocking you out of your casting with a puny little ice needle. Of course, everyone should thank Dhaos for showing it to us with his Tetra Assault spell, which basically fires all three of the weakest spells in the game at you at once, knocking you off balance for the truly epic ass-kicking he's following it up with.
In Tales of Rebirth, it's possible for one with enough time and knowledge of the enhance/inherit system for equipment to make a weapon that makes the wielder cause 32 times more damage.
In Tales of Xillia, all elemental damage has a chance to inflict status effects on enemies. Light-element attacks have the chance to inflict the Confused status, which makes a combatant attack their allies. Milla gets a powerful Light element spell late in the game, a little bit before she can pick up the Aerial Casting skill. With her Double Jump, Aerial Casting is a game breaker on its own, since Milla can jump too high for enemy AIs to detect and attack her, and Aerial Casting keeps her floating there until the spell resolves. But once you boost her chances of inflicting status effects on enemies (usually by boosting her Intelligence stat), Milla is an absolute monstrosity against any group of multiple opponents, as she can get them to kill each other with ease. What's worse is that most of the powerful boss fights in the storyline (including the final battle against Gaius and Muzet) have them come at you in groups. Difficult boss battles become hilariously trivial when you can confuse them into using their Mystic Artes on one another.
In Tales of Xillia 2, Ludger's signature Corpse Shell mode is absurdly powerful, as it allows for combos that are only limited by the duration of the mode itself (Which is extremely long once you get all of the abilities that extend it), but most notably, maintains the damage bonus you get from exploiting an enemy's weakness for as long as you can maintain the combo, meaning it's entirely possible to almost a minute of time to exploit a 5X damage multiplier when it would normally fade away after a few seconds. Not even the strongest bosses in the game can live through it if you can activate it while the damage bonus is at its max.
The Combo Spell ability is another extremely potent ability, as it reduces the character's casting time proportionate to the number of hits they've scored. This basically means that characters with it can keep casting spells back to back to gradually decrease their cast time until everything they use triggers instantly, allowing you to completely fill the battlefield with spells that can keep even bosses locked down indefinitely due to the status ailments some of them can inflict.