Many dogs breathe 10 to 30 times per minute;for cats, the rate is 10 to 40 times a minute.  Dogs who are hot or exercising breathe faster and may pant up to 200 breathes per minute.  Panting and open-mouthed breathing are considered danger signs in cats because they don’t use panting routinely as a means to cool off the way dogs do. 

Monitoring Respiration

When your pet is resting quietly, anything other than quiet, effortless breathing requires medical attention and possibly artificial respiration.

Respiratory Signs What They Mean Call the Vet?
Effortless breathing, quiet to soundless Normal NO
Increased respiratory rate First sign of breathing problems YES, immediately, if condition is worsening.  If respiratory rate is increased but problem is not worsening, call the vet the same day.
Excessive panting or gasping; dogs stand with elbows outward, cats sit crouched with head and neck extended Emergency!Progression to early respiratory failure YES, immediately
Labored, open-mouthed breathing and blue gums Emergency! Pulmonary failure; pet is suffocating YES, immediately
Slowed, shallow, or stopped breathing, unconsciousness imminent Emergency! Respiratory collapse; prepare for artificial respiration YES, immediately

Shojai, Amy D. The First Aid Companion For Dogs & Cats. Rodale, Inc., 2001.