Dogs cough for many reasons, including allergies, tracheal disease (collapse), lung disease, or due to the lodging of a foreign material/object in the windpipe. Though not typically serious in and of itself, coughing may require urgent medical attention if it should persist or become more severe.
It is important to observe if there is a pattern to the coughing (mostly at night, during excitement, etc.), as this will help in the diagnosis. Repeated bouts coughing or choking, for example, requires urgent medical attention.
Dogs, much like humans, cough for so many reasons that it's hard to list them all. Worms (including intestinal parasites and heartworms), pneumonia, allergies, kennel cough, smoke, tumors, heart or lung problems, or even a collapsed windpipe are all possibilities. If you are concerned the coughing is due to something serious, contact your veterinarian immediately.
Keep in mind that coughing is the body's defense mechanism against some diseases and emergency situations and should not be controlled without medical advice. In fact, you should never use over-the-counter syrups that suppress the cough unless directed by your veterinarian. In addition, mild or minor coughs can usually be treated at home with medicine containing an expectorant. Consult your veterinarian for suggestions.
Placing your dog in a steam-filled bathroom can also alleviate the cough. This can be done for up to 15 minutes (with the shower off, of course), as long as your dog is not distressed by being alone in the room. Follow this treatment with coupage, which is the gentle striking of both sides of the chest with cupped hands, for 2-3 minutes.
Minor coughs should not last longer than a couple of days. If your dog isn’t better on the third day -- or is showing signs of other problems -- seek immediate veterinary care.