I would say that in writing, in particular, we shouldn't break the simple rules of grammar and spelling and many other basics. My reason for that is quite simple, if you writer "gramer, speling, n simpel" most readers (and definitely most agents and publishers) are going to stop reading right there. If your intent is to sell books (as opposed to writing stories for your own private entertainment), then you need to follow the basic rules that make you look like a competent writer in your chosen language.
Now, one of the "rules" in writing is to avoid "-ly" adverbs. Angrily, spitefully, joyfully, quickly, etc. But JK Rowling uses them liberally. (Stephen King says, with joking disapproval, that 'She's never met an adverb she didn't like.')
(The problem is discussed elsewhere on Writers; basically the issue is 'telling' the reader a state of mind instead of 'showing' them a state of mind, and they can feel quickly overdone.)
Breaking that rule might have prevented her from selling her first book more quickly, but eventually it was okay for the lesser literary sophistication of her young-adult audience.
So "no -ly adverbs" is a breakable rule. I think her books would have been better if she'd followed it, but, meh. Her imagination and story line obviously far more than make up for the issue.
Other and bigger such writing rules can be broken. For example, the Three Act Structure was derived from many hundreds of successful stories, and basically the three acts are "the beginning, the middle, and the end". The structure details what is typically IN each of these segments, at least in the majority of popular stories.
But you can break it. Shakespeare uses a Five Act Structure which contains twists in different places, and history suggests that works gangbusters. The "Hero's Journey" is another structure that works great. In the Three Act structure, we typically describe the protagonist's "normal world" first, and have an "inciting incident" at about the 1/8th mark, and we have our protagonist leaving their "normal world" about the 25% mark to deal with a disruptive problem at the end of Act I, and this marks the beginning of Act II.
But those have been severely compressed and expanded in the past. That can happen because a writer is awesome about creating a lot of plausible conflict in a story, and as long as there is something up in the air that readers are thinking about, a writer (like Stephen King) can basically go on indefinitely, because what we are reading is interesting and that carries the day.
That is the one rule you shouldn't break: You can't be boring. If I get tired of reading a scene and put the book down, that may just be me, being cognitively exhausted by my day, or mentally distracted by something else.
But if I'm actually bored with your writing, then after the second try I'm putting it down for good. I think agents feel the same; their professional time is limited, the number of manuscripts they get is more than they can represent, and they are professionals actively looking for reasons to drop a book and start the next one. They don't want to waste time.
They (professional readers like agents and publisher's first readers) are your litmus test. If your writing is interesting to them, and you don't have any (or many) mistakes that would break their reading reverie or make them wonder when you are going to make a point, you don't really have to worry too much about whether you are following the rules.
Remember, the Three Act Structure and other rules are basically derived from the study of successful stories; they are not mandates from on high, but a descriptive science, kind of like primitive chemistry. Because the stories existed long before they were studied to find commonalities, and they were written/told by story-tellers that used trial and error to find structures that kept their audiences captivated.
My advice (as a research scientist) is to learn and follow the rules, but if you have a great idea you believe will still captivate the audience, feel free to break them. But you still have to test if it works, and if you are proven wrong, find another way, or follow the rules.