Game Breaker / Arcanum: Of Steamworks & Magick Obscura
Apprentice training in any of the fighting skills grants +5 Speed to all weapons used by that skill. It only takes a single skill-point invested in it and can be trained by just about any town guard for pocket change. The difference is so massive it can go as far as grant five additional attacks with a fast weapon. In the case of one-use throwing weapons, it completely cancels AP cost of using them.
A minor one for technologists is the electric ring in the second level of the electric tech tree. It gives a +2 to Dexterity when worn. You can wear two. In a game with only 64 character points to give your character, four extra is a huge bonus, minus the two you spend to get there. If you're going for electric mastery, then it might as well be four more points. And you can easily make them for your companions, giving them on average at least one additional attack per round.
Essence of Intellect is an even greater point-saver for technologists. It's relatively cheap (100-500 gold), can be bought in just about any magic shop or gypsy stand, and it works even if your aptitude is 100 technology (but only for a very short time). How it saves points? It adds 10 Intelligence, allowing you to learn all schematics in any given tech branch from a baseline of 9. As long as the potion is active, all those schematics are available, and can be relearned by drinking another. You essentially get 10 free character points to spend on whatever else you want, like another tech tree for example. It also lets you unlock powerful end-game gadgets pretty fast, since that's 8-9 levels less to get access to specific items — a feat impossible when unlocking spells as a mage. It can even be used in the very first town, greatly helping with powering through the Beef Gate.
In the same way, the first fire spell, agility of fire, is the same for pretty much every fighting skill sans Firearms, as it raises the target's Dexterity, the stat which those skills depend on, by four, and the effect stacks. By casting it on yourself three or four times, you can gain mastery of any of those skills as early as at level 2.
The Explosives line for technologists becomes absurdly powerful if you invest in it and throwing. Almost all of the crafting recipes have materials which can be scoured from trash bins, they can be sold for massive profit, and the higher level schematics create deadly combinations. You'll have a character who can stun an entire room and then blow them all up before they know what hit them.
Puny Molotov is enough to throw your enemies all around, forcing melee fighters to waste all their AP to close in once again.
Throwable explosives by default are broken by the sheer virtue of costing 1 AP to use. Or no AP at all with the Apprentice training. As long as you still have supply in your backpack, you can keep tossing grenades until nobody is left standing.
The Looking-Glass Rifle borders on Good Bad Bugs. The rifle comes with few really potent properties. It has the longest range of all weapons, surpassing any possible form of attack. There are absolutely no range penalties when firing (it takes Master of Firearms with other guns to get this effect) and the weapon itself comes with additional +20 to-hit bonus, making it pretty much impossible to miss a shot, even while having just single point in Firearms. It's all balanced out by the fact the rifle deals 10-30 damage — a massive gap combined with so-so maximum output... unless you happen to have a version of the game where it deals instead 40-40 damage, while retaining all the other nice properties. That's about the amount of HP average mid-tier enemy has, so it's perfectly possible to waltz through the game up until T'sen Ang or so with this rifle. Combined with mentioned above explosives and you can take down an army all by yourself.
For melee technologists, Smithy is just as broken. Balanced swords can be created in the first town or have Magnus make them for you by the second. They have one of the the fastest attack rates in the game, but still have good damage. The next step up is the featherweight axe, which is slower but stronger. The axe can then be upgraded into the deadly pyrotechic axe, which pound for pound is pretty much the deadliest tech melee weapon in the game thanks to fire being such a broken damage aspect (it's also invulnerable to weapon damage save critical failures). The only things that outclass it are Infinity+1 Sword weapons. After that, you get to make the best tech armor in the game.
There is an unique sword called Sword to be found in Isle of Despair, used by one of the bandits in the fighting pit. Though it uses the same image as a Balanced Sword, it deals 10-15 damage and comes with Speed of 15. To put that into perspective, the Balanced Sword, one of the best melee weapons in the game, deals 3-12 damage and has Speed rating of 18, while the Feather-weight Axe does 1-16 damage and has a Speed of 12. In other words, Sword deals — at a minimum — greater than average damage than either of those weapons and has attack speed comparable to both. In fact, only a handful of weapons deal minimal damage equal to or above 10. Due to its Speed, it can outdamage the Pyrotechnic Axe, without the standard downside of destroying or badly damaging armor of attacked people. The best part? It has neutral aptitude, being, well, a generic sword, so just about any melee character can use it. The only drawback is that it suffers weapon damage, unlike the axe, so all the Demonic Spiders the axe will stop will trash the sword.
If you go the magic route and specialize in Force magic, you will eventually be able to cast the Disintegrate spell at half endurance cost. It will completely and instantly vaporize whatever it hits, essentially letting you run all over the place destroying anything that stands in your way, be it monster, NPC, or a door. It destroys loot, which is something of a downside, but there are a lot of things to kill that do not drop loot (or drop worthless loot).
The fifth-level time magic spell tempus fugit speeds your party by a factor of two, and slows everything not in your party by the same factor (no saving throw, no immunity, magic resistance does not apply). It has a large up-front cost, but the cost to sustain it is trivial. It's every bit as broken as you would expect for something that increases the number of actions your party gets per enemy action by a factor of 4.
Fatigue slowers halve the fatigue cost of all spells while they're active. Combine that with fatigue-restoring potions, and you can throw around several hundred fatigue points worth of spells without rest. And yes, that can be combined with Force mastery, which allows you to Disintegrate the entire population of The Very Definitely Final Dungeon.
The dog. Really high damage, fast attacks, and usually hits. For added cheapness, he even automatically gets the mastery bonuses that you have to either pay or work your ass off for. Makes combat a bit too easy, and kill-steals like you wouldn't believe. He can even bite open doors and chests inflicting only minor damage to himself. You do not need keys or unlocking skills/magic anymore. All it takes to get it is reaching Ashbury (which can be done right after hitting Tarant or Blackroot or even walk there without using train) and either pay pocket change for the damage the dog caused or kill the gnome kicking the starved animal — it won't even trigger aggro from town guards.
Every combat skill has a matching uber-weapon, almost all of which become available at an appropriate stage of the game. However, Throwing specialists can obtain the Aerial Decapitator around halfway. Finding it may be a Guide Dang It, but after that you have a one-hit killer that requires no ammo and doesn't break. It's also one of the fastest weapons, so even if the first hit isn't lethal, your opponent probably won't be able to retaliate before the next one does the job.
Even though it's somewhat late-game, the healing mechanical spider gifted to the PC by returning the camera from the crash site counts. As soon as you have it, forget any possible need for any type of healing. One spider, so long as you can keep your party alive, will heal anything short of a maxed-out mage. And the late-game aspect is dropped if you can navigate to a certain mountain passage and cross it in reverse direction.
In mods that restore cut content, Clockwork Physicians (healing mechanical decoys) are even more broken than the aforementioned spider. In exchange for being far weaker and incapable of combat, they're much lighter and move faster. The parts to make them are also cheaper and much more common, and the recipe makes two at a time. You can have a swarm of healing bots that will make you and most of your party all but immortal. They also sell pretty good in a pinch.
Ristezze, the junk merchant in Shrouded Hills, uniquely carries the key to his shop inventory on his person. With some Save Scumming or a point or two of Pick Pocket, you can steal this key and gain permanent access to his inventory. The inventory itself is fairly worthless, being junk, but he keeps his gold in there, too. That works out to 1000-2000 gold each time the inventory resets, which you can do simply by walking away and advancing to the next day. Never again will you worry about money. Furthermore, he can be used to identify items for free, simply by dumping them in his inventory then asking to barter. The items will be identified and you can steal them right back. No need for scrolls or gypsies.
Once you find the Necromizer schematics, you can turn some of the most dangerous enemies in the game into your eternal zombie companions. And if they die, just revive them again. The ingredients can be bought or stolen from shops, so you craft an endless amount, for free if you have the lockpicking skills to rob them.
As soon as you visit Tarant or Blackroot, you can take a train to Ashbury and then dart straight to Vendigroth ruins. With some speed potions you can run past most enemies and get yourself the components and schematic for what may be the best firearm in the game, but if you are willing to pack a couple of invisibility scrolls and explore further, you may also get a chemical that raises all your stats by 1 permanently, and an army of battle robots.
Backstabbing skill for melee fighters. Each character point put there lets you deal additional 4 damage when you attack your target directly or diagonally from behind with a dagger (and, if you have an Expert training, a sword and an ax). Fully maxed out, it equals 20 bonus damage, the same as when maximizing your Strength, only the latter requires 12 additional points on average while the former just 5 (since it depends on Dexterity, the same stat as Melee and Dodge skills), minus a couple of action points to actually get behind them. The realGame Breaker, however, happens if the target is unaware of you or stunned (by a lucky hit, or a grenade, or level 2 Mental spell), in which case the bonus damage is multiplied by 5 (up to freaking 100) and, with Apprentice training, ignores armor, effectively allowing you to administer One Hit Kills to all but the toughest enemies. On the other hand, critical backstab fails are basically you accidentally committing seppuku, so Melee Mastery is recommended.