The Arcane Warrior is pretty much totally invincible once you have Shimmering Shield. You barely need a party on the hardest difficulty with this spec, even the hardest bosses can be easily worn down by yourself.
The Mage spell Mana Clash drains enemy demon, abomination, or spellcasters' mana pools, and does Spirit elemental damage (which few enemies have a resistance to) in proportion to the mana it drains. It is entirely possible to one shot even the strongest of enemy mages with this spell, especially when empowered by its prerequisite Spell Might. It can usually take out entire rooms full of opponents in a single shot, which basically allows you to walk through the Circle Tower quest (where about 90% of your opponents will be vulnerable to it). It also does more damage to the victim if they have larger mana reserves, which means it allows you to make mincemeat of magic-wielding bosses (sometimes you can even kill them with a single shot if you use the aforementioned Spell Might). A lot of missions in the game become much, much easier if you bring along a Mage who can cast Mana Clash.
Crushing Prison stuns enemies while dealing damage (and you're free to deal plenty more from your next attack).
The room-clearing Storm of the Century (a combination of AOE's Tempest and Blizzard). Combine Tempest, Inferno, Blizzard and Earthquake and you'll see why you are just overdoing it.
The Blood Magic spell Blood Wound, which boils the blood of all nearby enemies, as well as paralyzing them for the duration of the spell. Yup, another room-clearer, and one that makes all other damage spells parlor tricks in comparison. Some strategy guides actually advise against spells like this, since they turn pretty much every battle into walks in the park. The only limit is that enemies without blood are not affected, but there aren't enough of those to push it out of gamebreaker status. Also? This spell has no friendly fire.
There's some even more devious spells that the game knows go together in a Game Breaking fashion, and even mention it in the spell descriptions. There's Sleep, Horror and Waking Nightmare, Horror causing damage to enemies if they fail a resistance check, and Waking Nightmare causing, among other things, enemies to stop attacking you at least (whether through a fear effect or a temporary alignment change), and turning on each other at worst, also requiring a resistance check. However, if you successfully cast the Sleep on them first, they automatically fail the resistance check. At this point, your choices are, kill them immediately, or sit back and watch them turn on each other. Pass the Popcorn, please.
Force Field. Basically you get a tank character (some warrior, Alistair or Shale usually), get them to spam aggro generating abilities (as well as use aggro "aura" effects such as Threaten and Stoneheart) and once they have the unbreakable attention of every enemy on the screen, put Force Field on them to make them invincible. So, while 10 skeletons beat on your invincible tank character, your party is free to proceed as they please with no resistance to speak of.
Death Hex and Death Cloud, when combined, change from "Critical Hits For Others" or "Damage Over Time" to "DieBitch".
Once you have acquired the Dalish Elves' assistance, they ask for you to donate basic crafting ingredients. Like all donations to your forces, you get 10 xp for every item you donate. One of the items you can donate is elfroot, which you should already have plenty of and can get lots of for cheap at many merchants...but what makes this not only useful but ridiculous is the fact that there is a single merchant in the base game that can sell you unlimited amounts of elfroot, in stacks of 99 (990 xp), for a pittance. It's Valathorn, the merchant...in the Dalish Elf camp. "You do not talk about Grey Warden Camp", anyone?
"We were giving the treehumpers' own stinking weeds back to them, and for it they made us gods."
The ingredients for making Potent Lyrium Potions are much cheaper than what you can sell them for, making this an extremely easy way to make money. Even better is that you can buy infinite amounts of three of the four ingredients from a single vendor. After working up a nice nest egg using this, you can use the above-mentioned elfroot donations...or you can just donate to the Arl's knights directly, saving yourself the trouble of traveling back and forth, which would be the only inconvenience, since money has lost all meaning.
From the Feastday Gifts DLC we have the Qunari Prayers for the Dead: an item that can be used over and over so long as Sten in your party and conscious. It's effect? Bringing any fallen party members back to life. Very handy in some of the tougher boss fights. The real game breaking element is that you're invincible during the cutscene, and if you watch it all, the party is restored to max health and mana, so as long as Sten is alive, your party is essentially immortal. This can be cheesed to astonishing effect.
It's quite easy, with the right build, for a Rogue to obtain a 95% chance to dodge. This is just as overpowered as it sounds, and makes most non-Mage enemies a joke.
Dragon Age: Origins - Awakening
In Awakening characters can choose a third specialization at level 22. This is unbelievably broken, given the fact that on the second playthrough...you can get two of the new (incredibly overpowered) specializations. (Even Keeper, which doesn't match up to Battlemage, the other new specialization, isn't bad when a player knows how to use it.)
You can buy a paint job for your shield with the emblem of the Legion of the Dead. Not particularly nice looking, but it gives a whopping +20 to all attributes. (This is apparently a bug that has remained unfixed except by unofficial mods, as every other heraldry adds only +3.) That's even more than it sounds. As a comparison, the Legion of the Dead heraldry adds a total of 120 ability points. If you max out your level at 35, you will get a total of 102 ability points from leveling up.
Accuracy coupled with Aim, high dexterity and some rapid aim gear turns archery from the inferior rogue build (and rogues aren't that great to begin with) into having a crit rate of over 100% and tripling the damage you did before. What does this mean? You're oneshotting mooks at max attack speed with autoattack and are essentially untouchable. This allows you to even solo the hardest encounter in the game (The Harvester on Nightmare) with minimal difficulty. Which is good considering your allies for that mission are terrible and built wrong.
Sword and shield is also extremely powerful when stacked with dexterity, dodge + % and defense+ items. Making the tank nearly impossible to hit, add spell resistance from Templar, enchantments, auto-health regen as well as awakening's broken carapace skill (First 15 sec of skill makes you immune to damage, the second half absorbs a percentage of damage that actually manages to land). For even more fun, give the tank a good dagger to take advantage of that high dexterity.
Dragon Age II
The Gravitic Orb spell is fun to abuse. It will cause all foes within its wide range to move at a snail's pace, allowing you and your companions to pile blow after blow on them without fear of serious retaliation. Foes at the epicenter of the spell are so slow that they might as well be paralyzed. The spell turns almost any boss fight into a Curb-Stomp Battle. For extra fun, you can clump all your foes at the center of Gravitic Orb using Pull of the Abyss, and take advantage of their inability to spread out from one another by finishing them all off with an area of effect attack, like Firestorm or Cone of Cold.
Dual Weapon Rogue -> Assassin specialization -> Assassinate -> Overkill -> amped-up Cunning = one-shot just about anything that isn't a full-fledged boss. The Assassin specialization also gets Pinpoint Strikes, which turns every attack into a critical hit, and a passive ability that doubles the critical bonus granted by Cunning. Anything that survives Assassinate can be cut down by Pinpoint Strikes in seconds. And then you can have Anders or Bethany cast Haste, and Hawke will be hitting enemies so fast that their health bar will be glowing white from all the critical hits. Adding to this is the Duelist specialization, which works to essentially make Hawke nearly untouchable in combat and able to tear down single opponents in seconds. Specc'd properly, a Dual Weapon Rogue Hawke with Assassin and Duelist specializations can tank and inflict horrific amounts of damage by him/herself, becoming an almost literal One-Man Army.