When riding, I often am.
I do yoga and meditation, and understand that breathing through the mouth has all kinds of negative effects. It also looks bad. (I try to obscure the fact that I'm breathing through my mouth by only taking gulps of air when I need to, and holding my mouth nearly closed -- whenever I see a slackjawed cyclist gasping up a hill, I think of the cyclist in Triplets of Bellville.)
But I simply can't get enough air through my nose when cranking. Flaring my nostrils as wide as possible helps, but not enough. My nasal passages aren't obstructed, they simply don't admit enough air.
Anyone have any thoughts / observations / etc?
(PS. "mouth breather" is also colloquial for "a stupid person; a moron, dolt, imbecile.")