When it is outside the norm of what is usually seen for your dog.
Different breeds of dogs will pant different amounts. There is an element of individuality in how much any one dog pants. The important thing is to get a baseline level of your dog's behavior from a young age, and then if you see a major change that can't be attributed to something like exercise or anxiety, take them into the veterinarian for a professional opinion.
If this is a new development, definitely see your veterinarian about it, Alander said, as it could be an indicator of underlying illness.
However, if it's been a typical behavior for your dog from a young age then there isn't much cause for concern. Different breeds of dogs will pant more than others, sometimes dependent on the size of their noses as smaller-nosed dogs might be more dependent on breathing from their mouths (think pugs.)