In order to be game breaking in the first place, you have to be able to define how the game can be broken. This is the problem with an open-ended game like DF - with no real goal, you can't say that anything really makes it too easy to reach that goal. There IS no goal to reach, aside from the ones you set for yourself. If all the more you want from the game is a mostly non-violent, fantasy version of The Sims, you're going to play the game entirely different from someone who plays with Dig Deeper and refuses to use bridges, quantum stockpiles, or traps.
Give us your definition of what means something has broken the game.
Well, in most builder games, survival, growth and economic success are usually positive indicators of your progress.
Some of the 'tricks' or tools listed in this thread can make achieving success rather trivial...which makes it boring...and less Fun.
For some people, it's hard to stop themselves from using all the tools given to them by the game.
For example, it's perfectly natural to want to put a drawbridge, walls, moats and traps at your fortress entrance. Once you put those in place properly, your fortress is basically impenetrable. It doesn't take that much effort.
I remember the first time I played this game (not long ago). I was really excited when a metal Colossus had appeared and started tromping towards my fortress. I had prepared my military for a couple years, but I wasn't sure how they'd do. Then I was severely disappointed when the Colossus got captured easily by a cage trap. WTF! Every goblin siege was easily defeated as well by my defenses. I didn't even need my military at all. When I did finally open my defenses to let my military try out their skills, they rampaged through everything because I had prepared too much.
I don't want to have to intentionally screw myself over to create some challenge. That is kinda weird to me, although, it is a game mechanic you find in other games.
By the way, trade success is ridiculously easy too. It doesn't take long before you can build your craft industry to the point where you can easily buy out every single trade caravan completely. You're basically overflowing with 'cash' and nothing to spend it on. After a few years, your fortress is bursting with crafts, food, drink, top tier weapons and armor, etc...everything you could possibly need.