When to crop, It's not just about the rule of thirds!
Crop to....
 Straighten Horizons
 The Human eye can detect a difference of 1/10,000^{th} of an inch.
 Eliminate distractions along the edges of the photo
 Zoom in to magnify the subject (much better than using "Digital Zoom" in the camera")
 Fit the subject to the "Golden Ratio"
Examples
Straightening Horizons and zooming
Cropping for Printing
It is helpful to know what the aspect ratio is of the images your camera saves at...
 35mm film has an aspect ratio of 3 to 2 (Most DSLR's adhere to that ratio)
 There are some cameras that use a 4 to 3 ratio (same as the Old tube TV's and monitors)
 Some Cameras use the wide screen TV format of 16 to 9
 And! Some camera use a 1 to 1 aspect ratio (A Square) and others 5 to 4
 And, yes some digital cameras will yet you choose! 3 : 2 or 4 : 3 or 5 to 4 or 16 : 9 and even 1 : 1
NOTE:
If you change the images aspect ratio to make a print with a different aspect ratio, say, 5 x 7 or 8 x 10
You WILL LOOSE part of the image! There is no way around it… Crop creatively!
The Golden Ratio ~ 1.61803398874989484820... Derived from the Fibonacci Sequence
The Golden Ratio can be calculated quite accurately from a formula derived from the following construction.
The actual value calculated is an irrational number = 1.61803398874989484820... (etc.)
Now consider the Fibonacci Sequence...
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...
Where the next number is found by adding up the two numbers before it. Here's another way to look at the numbers...
To "get" close to the "Golden Ratio" divide any number by the previous number... the larger the numbers, the closer you get to 1.618033988749895
A 
B 

B / A 
2 
3 

1.5 
3 
5 

1.666666666... 
5 
8 

1.6 
8 
13 

1.625 
... 
... 

... 
144 
233 

1.618055556... 
233 
377 

1.618025751... 
... 
... 

... 
What does all of this mean?
The Universe that surrounds us is built from physical "constants" and common values from number sequences... and we are part of the universe. So, if we compose our photographs using the Golden Ratio, the more balanced the composition will appear to the human brain, the mind's eye!
Bottom Line
Trust your Instincts, verify by....
Using the rule of thirds and/or the Golden ratio to compose your photographs!
Photoshop Camera Raw
When using the crop tool, right click on the canvas to popup the "crop tools" requester and choose Show Overlay. Camera Raw only displays "The Rule of Thirds" overlay.
Lighroom
Choose the Crop Tool...Lightroom can display the Golden Ratio solutions... Golden Spirals, The Golden Ratio, diagonals, triangles, plus the rule of thirds and grids.
Press the letter O to cycle through grid overlays in the crop area.
Press Shift plus the letter O to rotate the overlay displays.
You can also find the Crop Tool settings in Lightroom using the
Menu: Tools > Crop Guide Overlays
Since Photoshop CS6
Grid and Crop Tool Overlays have been added to the Photoshops Crop Tool
This is CS6's Options bar for the Crop Tool...