Certain operations, when performed on an image, cause a small amount of data loss. While performing these operations once or twice may not cause any noticeable loss of quality, repeated application can cause drastic changes.
Bleeding
When an editing application is used to modify an image, the compression to JPEG can cause some of that information to bleed into other areas when the image is compressed. In this example the word BLUR using different colors was written to an image and then saved as a JPEG. Periodically, the same color text would be written, such that in a lossless environment the images would be identical. The same process was run using the PNG format.
While this is certainly an extreme example, this happens to a lesser degree any time you modify a jpeg and resave it. If possible, it is best to edit an image using a lossless compression, or no compression, and then save it as JPEG or other lossy format after you have finished.
PNG after 125 edits

JPEG after 25 edits

JPEG after 50 edits

JPEG after 75 edits

JPEG after 100 edits

JPEG after 125 edits

Rotation
Rotating an image causes the image to be resampled, thus data is lost. This will happen even if you rotate back to the original orientation. The exception to this are 90 degree rotations since they do not need to be resampled.
If for some reason you need to rotate an image but aren't sure of the angle, save a copy of your work first. Rotate the image until you get what you want, while keeping track of how much it's been rotated each time and in what direction. Then go back to the original and apply the total rotation once to the image to minimize data loss.
For example, lets say you rotate an image:
- 45 degrees right
- 4 degrees right
- 2 degrees left
- 1 degrees right
- .5 degrees left
Then the original would need to be be rotated (45+4-2+1-.5) = 47.5 degrees right
360-degree Rotation
In this example, the PNG file from the previous example was rotated in 72 degree increments, until it had been rotated 360 degrees, then cropped to remove dead space. Even though this image has only been rotated a total of 5 times, the data loss is immediately evident.

720-degree Rotation
After 10 rotations, chunks of data from the word BLUR have begun to break away from the bulk of the wording.

360-degree Rotation Without Expansion
Here is what happens if you rotate a file 360 times using 1 degree rotations without using image expansion:
