The July, 2008 Airline Pet Travel Report contains pet incidents for the month of May, 2008.
Alaska Airlines lists the injury of a dog (possibly a golden / lab) that injured its mouth trying to chew out of its kennel.
Continental lists the deaths of three dogs. All three were brachycephalic, or short nosed dogs. In none of the cases were there any obvious signs of trauma. Two of the necropsies listed the animals as overweight. The necropsy of a three year-old English Bull dog that was found deceased in Houston, TX from San Juan, Puerto Rico states "He may have gotten excited during transportation causing him to become dyspneic resulting in a cardiovascular collapse."
Continental also reports that they transported 8,993 pets by air during the month of May.
Skywest lists the injury of a puppy who was allowed to travel in a kennel that was not airline approved. The kennel fell apart during unloading in Salt Lake City, Utah and the dog scraped its nose and injured its eye.
United lists the death of an English Bulldog in route from Los Angeles, CA to Boston, MA. But does not list any further details.
Interesting to note that all the deaths were from short-nosed dogs this month.
Source: July 2008 Air Travel Consumer Report.