Apparently the traditional "Rule of Thirds" in photography is getting bashed lately because it can cause a photographer to not think outside the box, and severely limits creativity, according to some. Personally, I think any RULE will cause the same effect. So maybe lets not call it a rule. How about a "tool" to be used in SOME instances. A "rule" can be limiting in that photographers feel they MUST abide by it, but a "tool" means it is just one thing in your kit, along with many other tools. Now it doesnt feel so constraining, does it? What WOULD be constraining is throwing the tool away completely and never using it, because now your compositional tool box just shrunk.
I have been analyzing my own photo compositions lately in an effort to better teach people how I see the landscape through my viewfinder. To be honest, I never think of any rules at all when I am composing a photo in the field. My eye just kinda knows when the scene in my viewfinder feels balanced and "right". Kinda hard to explain, which is why that probably would not be a great way to TEACH others. Just as a beginning guitarist learns cords that will later be used to create original pieces, you have to start with some basic ideas, or "tools" that you can alter alter and customize to be YOUR signature style.
Here an an example photo of mine that I really like. Aside from the colors and the light, which I really enjoy, how is the photo COMPOSED? Keep in mind, none of this went through my mind in the field. However, looking at it now, it is kind of a mashup of several compositional principles. The "rule of thirds" can be seen horizontally in the placement of the frosted tree line and the mountains, but not vertically. Vertically the mountains are placed as one strong focal point DEAD CENTER, so the rule of symmetry would be more applicable there. Lastly, there is also CONVERGENCE in the clouds as the lighted lines of clouds generally draw you towards the mountains.
Point being: no compositional principle is a "rule", but none should be banned from your kit either, as some suggest. Many of my photos are traditional "rule of thirds" photos, many are not at all, but MOST are a blend of several compositional tools. This is the way I teach it to beginners. I will give you a fair amount of compositional "tools", none are "rules". You take the tools with you and what you eventually build as an artist is up to you.