Here are some extracts from various online photographic contests about the amount of digital improvement that is accepted by them:
Nature Conservancy:
All photographs should accurately reflect the subject matter and the scene as it appeared. Photos that have been digitally altered beyond standard optimization (removal of dust, cropping, reasonable adjustments to exposure, color and contrast, etc.) will be disqualified. Multiple exposures that have been combined to produce a single "High Dynamic Range" image are acceptable.
Smithsonian:
Cropped photos are eligible in all categories. We do not accept digitally or otherwise enhanced or altered photos, except for those entered in the Altered Images category. Minor adjustments, including spotting, dodging and burning, sharpening, contrast and slight color adjustment or the digital equivalents, are acceptable for all five categories. If the judges determine that a photographer has altered his or her photo, they reserve the right to move the photo to Altered Images or to disqualify it.
http://kids.nationalgeographic.com/kids/contests/photo-contest-rules/
• Minor burning, dodging and/or color correction is acceptable. Cropping is acceptable, as are fish-eye lenses. Any changes to the original photograph not itemized here are unacceptable and will render the photograph ineligible for a prize.
• Mounted or framed photographs are not acceptable.
http://photolisticlife.com/photography-contest-entry-form/2012-photo-contest-rules/
Only minor burning, dodging and/or color correction is acceptable, as is cropping. High dynamic range images (HDR) and stitched panoramas are acceptable.
Images may be digitally enhanced to remove spots or scratches, but not manipulated. Entrants can enhance the picture to make it brighter, clearer etc, but not manipulate the content.