Question: I always hear a lot about The Rule of Thirds. I'd like to know more about other 'tried-and-true' composition techniques (not special effects) that can make a photo more interesting.

In particular, I'd especially like to know:

* The name of the technique
* Any particular types of settings the technique is particulary useful
* Interesting ways to 'break' the rule

Answer: 
While this isn't a duplicate, this can essentially be answered by linking to a few questions we've collected regarding other composition techniques (thanks largely to @JayLancePhotography!):

* [Bakker's Saddle](https://photo.stackexchange.com/questions/11450/what-is-bakkers-saddle)
* [Rule of Odds](https://photo.stackexchange.com/questions/11475/what-is-the-rule-of-odds)
* [Diagonal Method](https://photo.stackexchange.com/questions/11060/what-is-the-diagonal-method-and-should-i-use-it-instead-of-the-rule-of-thirds)
* [Golden Ratio](https://photo.stackexchange.com/questions/8965/what-is-the-golden-ratio-and-why-is-it-better-than-the-rule-of-thirds)

Searching the [composition](https://photo.stackexchange.com/questions/tagged/composition) and [composition-basics](https://photo.stackexchange.com/questions/tagged/composition-basics) tag provides a wealth of knowledge.
For interesting ways to break a rule, learn why the rule works and break it when you want to achieve opposite effect. For example, break the [rule of odds](https://photo.stackexchange.com/q/11475/4390) when you want to stress symmetry and dullness of a scene.