This article is from the Canine Medical Information FAQ, by Cindy Tittle Moore with numerous contributions by others.
Dogs that breath noisily may have a serious health problem. For
example, some animals have an elongated palate, which prevents them
from breathing properly. The animal can also have a hard time drinking
and eating. This also can affect the heart since it has to work extra
hard to breath.
If your dog has this problem check with your vet. There is an
operation that can correct the problem of elongated palates. In any
case, dogs should not be constantly panting and breathing noisily, so
a vet check is in order.
In general, breathing anomalies should be investigated: noisiness,
wheezing, excessive panting, excessive coughing.