Top left to bottom right is the most common example of this, being the direction we read in:
Primary diagonals running bottom left to top right:
and although these are less common, I find that if I am consciously composing an image, this is a diagonal I am really drawn to:
Of course, as Kat says, the degree of the angle affects the overall image too. With the examples above, the olive branch (and the toes) are a much more dynamic diagonal than the starry path.
Multiple diagonals add an additional layer to a composition. Here are a few I found:
I love how the zigzag draws your eye from the snow capped Alps, over the Mediterranean, landing at the beach (or do you start at the beach?).
|and less dynamically....|
For me, the natural starting point for the image above is the bottom left hand corner, moving to the right and then back left as your eye progresses up the stairs. What about you, how do you read it?
I love the sense of movement that diagonals create in an image. Many of these examples are naturally occurring diagonals but when I'm composing an image I do consciously look for diagonals to bring interest and movement and create them where I can (for example the little toes in the bath).
I think diagonals are also really intriguing because although they guide your eye, different people read them in different ways - on the last image, I'm going up the stairs in the way I described, but what about you, are you with me or starting at the top, on the right or left? All of these things affect the overall impact of an image and how it is interpreted by the individual eye.
You'll find lots of other examples over at Exploring with a Camera, so click on the link and come exploring. :)