Scot,,
i suffer from panic attacks with just this symptom, and thats the need to keep taking a deep breath. Its horrible. Whats not normal is the need to keep taking large sighs, which is what i do when im feeling particulary anxious.
It isnt normal to want to take deep breaths very often, so i would say if your doing that then its a sign of anxiety.
Are you having any other symptoms? or are you suffering from anxiety?