Chimchirorin, in all its forms. This minigame could be exploited in several different ways in the first game - with proper use of Save Scumming, one could get a nice chain of wins against Tai Yo in your headquarters, save your game at the inn right beside him, rinse and repeat. Alternately, a savvy player could use savestates on an emulator to quickly rack up hundreds of thousands in potch, trivializing the economy long before the endgame and allowing them to upgrade their party's weapons as soon as possible and buy incredibly-expensive equipment much earlier than normal. And through trial and error, a player could find that aiming the dice at a specific spot gave something like a 90% chance of winning rolls. The developers likely figured out the potential for game-breaking antics, as the game was nerfed in II (the game now works on a set pattern, the sweet spot from I no longer exists and the maximum bet is 3,000 potch instead of 9,999), but it could still be exploited.
In this game, there are a couple of exploits for taking a detour from the One True Sequence. Before going to the castle, go outside, alone, and run away from enemies until you find three BonBons. Easy kill, and hey, level 9! After that, you have a choice of going to Sarady either by yourself or with Ted. Go alone, you get the Fortune Rune (double EXP); go with Ted, you get the Prosperity Rune (double money).
McDohl's teacher, Kai, can be recruited relatively early from the game and comes complete with a broken ability. You can put him in the party with McDohl to use their combined Unite attack, which hits all enemies on the screen. Unlike most combined techniques, this one didn't leave either character unbalanced (which means that they would have to take a turn to rest, like Hyper Beam users in Pokémon did), and was incredibly spammable against all enemies, including bosses.
Using the fourth spell of the water rune and the fourth spell of the wind rune in the same turn created a powerful attack that damaged all enemies, including bosses, and fully healed your party at the same time! To say this was overpowered would be an understatement, and it only gets better when you realize that there is a stronger version of each elemental rune, and using the final version of the water and wind rune's last spells made this even more powerful.
The only limitation to this trick is how many free slots a character has but one of the best ways to win fights is to fill up the slots with nothing but Sacrificial Jizos (The Hero will have one less slot thanks to the Blinking Mirror but he's so good he probably won't use a lot of those items anyway). In fairness, there is practically no other way anyway to get through some boss fights, but this is why starting Suikoden II, item slots are limited to three characters.
Around the halfway point of the game after you defeat your father General Teo, you automatically recruit two swordsmen Alen and Grenseal. They allow you to break the game in a few ways: first, they have incredibly good stats, being both proficient in physical and magic attacks. Second, they have a combination attack with Flik that can deal insane damage to a single target without any drawbacks such as unbalanced status (Flik is also a Required Party Member for the final dungeon, so they can really make the final dungeon easier). Third, they come with a Rage and Thunder rune permanently attached. Not only does this give you free access to the strongest AOE and single target magic of the game, due to both units' high magic growth you can utilize the Fire/Lightning combination attack to pretty much burn your way through the opposition.
The Matilda Glitch is an infamous exploit that can be done right near the beginning of the game. Normally, the hero and their party are barred from passing through the Muse-Matilda border due to the warring factions at the time. However, by running up against the gate at the border, the player can push it like a box and move it forward, allowing them to get past it and enter the Matilda region. The enemies here are far and above the party's current level at that point, but if you can defeat a group of enemies (normally by spamming your most powerful magic attacks), your levels will shoot up by twenty or more.
Additionally, you can travel to the nearby Highway Village and get powerful accessories like the Fire Emblem, as well as recruit Humphrey and Futch by completing their sidequest. This nets you two characters who, depending on how much you leveled them in the previous game, may be leagues more powerful than anyone else in your army.
It's possible to break the Rock Climbing game by exploiting savestates to get you further up the cliff by constantly resetting to get higher dice rolls. Doing so allows you to get several powerful items much earlier than normal, including the Goldlet (one of the best defensive items in the game), Taikyoku Wear, permanent stat boosts and party member-specific items that boost their Unite attacks.
Knowledge of the trading system will allow the player to do things like buy Gold Bars from one village and sell them gobs of money (up to three times its value) in Highway Village long before the endgame, thereby trivializing the entire concept of earning money.
Sheena can become one of these at higher levels, and there's also Georg Prime to consider.
Killey, for the same reasons as Sheena, except he's even more powerful.
Recruiting the main character from the first game. The Soul Eater Rune is as awesome as ever.
Because of how the Rune Unites work, one can place a slower character in the first party slot to make the whole party cast up to five Rune Unites in one turn! Not bad for a game where mages are pretty useless by the late-game.
Double-Beat rune, especially when compared with other runes or used by anyone with three rune slots. Add in Fury Rune and Double-Strike rune and you'll pretty much have a character who can get all, if not most action in battles. Even more so when you realize you can get Double Beat way early in the game, if the Random Number God is merciful on you.
Some surprising characters are effectively game breakers if you abuse abilities, titles, equipment etc. Quite possibly the best person in terms of pure destructive terror is Alanis, an optional 15 year old girl. Who needs a True Rune anyway?
Juan and Emily. The battle system allows characters with the right skills to attack several times per turn, and they can move on to other enemies when their enemy falls before their attack string is finished. These two can get more than 10 attacks per round each, with each hit doing roughly 400 damage. Add to that the fact that Juan has a Waking rune attached permanently, which means he's doing at least double damage when he wakes up. The downside is that this means he's going to be sleeping for at least the first round, but you can equip accessories that nullify sleep to just have them demolish absolutely everything you encounter within one round. Even bosses don't last very long against that.
Mounted units (Hugo + Fubar; Futch + Bright; Franz + Ruby) are the bests tanks of the game. You can load the monsters accessory slots with medicine and have them use it when necessary without wasting turns, as their rider will attack the enemy on the same turn anyway. The pairs also shares the total HP and attack power.
Hugo mounted with Fubar is one of the strongest characters of this game. While he can't exactly out damage both Juan and Emily, he does have access to a second unit who can do anything while Hugo does all of the attacking. Simply give whatever consumable items at Fubar while Hugo does all of the work.
Kika and her triple-damage, non-missing, infinite-use Falcon Rune. Throw in Ted (most powerful spellcaster, bar none) and Snowe (gets an ABSURDLY powerful Combination Attack with Lazlo), and you've got a team that simply can't be stopped.
Reinhold's Training Hall, where the enemy levels are based on the highest-level member of your group, is a easy way to grind you characters to level 100 in a couple hours.
The "Treasure Hunting Mini-game", as it lends you to rare equipment, a Encounter Repellant Rune and to high-level magic runes. The first Treasure map, that Rene gives you for free, leads you to a Rage Rune, a more powerful Fire Rune.
By starting the game with a Clear Data of Suikoden IV with the 108 Stars of Destiny recruited, you can get Lazlo as early as Chapter 12. Remember how his Rune of Punishment was balanced in IV by draining some of his HP with every spell cast? Well now it doesn't. Instead it heals him with every spell cast. He also has good physical attacks and combination attacks on top of his overpowered rune.
Not to mention that he counts as a "plot-relevant character" (despite being just a guest), and thus cannot be permanently killed in battle.
The Elemental Sword Runes are extremely useful as a way to keep a character on his or her element, which greatly increases their performance.
Magic Absorb Runes. In previous games, they were barely worth equipping, only restoring level 1 MP a portion of the time, as well as dropping the wearer's accuracy. In this game? They restore the lowest level of expended MP (which means they can recover level 4 MP if all your lower-level spells are full up), the effect works every time, and there's no accuracy lost. The only downside is that they can only be equipped to the right hand (which prevents people with Runes locked on that slot from using them, such as Viki and her locked Blinking Rune), but anyone that CAN use them effectively has infinite MP. And given how utterly broken magic can be...
Zerase and Levi become the best tag team duo in the game with these. Zerase starts with the powerful Star Rune and has a second slot free for whatever suits your fancy (Such as a Flowing Rune) while Levi has two free slots to do whatever he wishe swith - Rage for raw damage, Cyclone to heal the party and damage foes at the same time, or Mother Earth to completely nullify enemy spells. Basically, once they're both up to speed, the rest of your party becomes little more than glorified human shields.
Once you understand how to uses them in army battles, the Beavers prove to be quite lethal: it is entirely possible to sink 40-50% of the ships with the one beaver unit: that means that more than 6.000 trained soldiers where slaughtered by one hundred armed beavers: you don't mess with Falena's Beaver.
Zerase. She has a powerful rune that allows her to rain immense amounts of damage on the enemies, has enough magic to cast the more powerful spells an adequate number of times, joins automatically as part of the story, and comes pretty early too. To quote a rather amusing comment from a walkthrough; "If you equip her with a Magic Absorb Rune on her right hand and a Flowing Rune on her left, the game will basically just give up and let you win."
Viki has her unique skill, Chain Magic. Chain Magic, when activated, will give Viki a second casting of her chosen spell on the same round, ABSOLUTELY FREE. Load her up with a Lightning or Thunder Rune, give her a couple of Lightning Amulets to max out her Lightning attribute, pump Chain Magic up to SS rank, and Viki can potentially put out just about the most damage of any single character in the game.
Richard can block, counter or dodge some 90% of the physical attacks in the game. Don't bring him along if the boss mainly uses magic though, as he will most likely die. Give him a Firefly Rune and you can breeze through most battles.
Raven's unique Raven Rune grants him 100% evasion to all physical attacks while in a dungeon. And yes, this even includes "outdoor" dungeons like Waterfall Basin and the final ruins. Give him a Firefly Rune and watch enemies desperately try to even hurt him while you pummel them to death.
Georg Prime has great stats and starts out with a rune that increases his critical rate and gives him a small chance of instantly killing enemies. There's a reason the game significantly limits your ability to actually put him in your party.
Ernst's Beast Rune has his second skill where everyone gets an Unbalance status. It works 100% even at the FinalBoss. The Circle Formation offers a similar benefit with its Form Skill, Defensive Circle. You can only use it once per battle, mind, but you don't need to spend a turn setting it up either. It's worth noting that not only are unbalanced enemies unable to act that round, but they can't dodge attacks either.
Any character with three open rune slots can easily be turned into a murder machine, thanks to a number of powerful damage-boosting runes, such as Power (50% Attack boost in exchange for halving Defense), Double-Edged (doubles damage given and received), and Boost (increased damage output for 3 rounds, but then drops to 1 HP). Those three runes? THEY STACK. Load them all on the same character, and that's roughly 6x damage. Get an entire team of fast-enough characters with this setup, and pretty much every battle will be over before the enemy can do anything (which is a good thing, since anyone with this setup will die if an enemy even looks at them funny.) Combine them with the aforementioned Unbalance-inducing skills above for absolute hilarity.