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.
Apart from rules of thumb like the rule of thirds, there are mand general compositional principles which are generally the same in all art forms, things such as balance, space, pattern, texture, lines and shapes, light and shadow.

Very common compositional techniques in photography that I can think of

* leading lines - leading the viewer's eye through the image
* patterns, and I think even more importantly broken/interrupted patterns
* selective focus or color (attracting attention to the subject by blurring/desaturating the background, I guess vignettes fall into this category
* negative space
* unusual perspectives - images of objects from a viewpoint not usually seen (ant's eye view of a flower or pet), extreme wide angle or tele shots
* framing - leaving space in front of the subject if moving, or looking out of the picture
* with wide angle images, having strong foreground interest
* use of strong contrast, bright objects or bright colors to draw the viewer's eye
* lines - diagonal lines and curves are more "dynamic", while vertical ines imply strenght and horizontal lines are more static and calming
* horizon - generally should not be placed in the center of the image, either the foreground or sky should be given more space - one exception would be water reflections where dead center often works
* in general the main subject should be off centre (rule of thirds or otherwise) but usually needs balancing by other objects
* triangles generally make for strong compositions

I think the best images are ones the attract the eye even when looking at a small thumbnail, and you're not sure what the subject is, but the eye is attracted by a strong pattern, shape or color.

The article below is worth a read. It covers a lot of the above, and more.

[Wikepedia article Composition](http://en.wikipedia.org/wiki/Composition_%28visual_arts%29)

Also, you might want to look into Gestalt Theory, very relevant to photographic composition. For example here: [PDF](http://www.imageinnside.com/wp-content/uploads/2010/09/Gestalt-Theory-and-Photographic-Composition..pdf)