I'd never really thought that much about breathing until I read "Chi Running" (as recommended by Terry, and an absolutely fabulous guide to running). I'm still working on my patient breathing while swimming, but where I noticed an immediate change was in my cycling. I felt better, i recovered quicker from hard efforts (climbs or sprint intervals), and I even increased my cruising pace by a few tenths of an mph (it doesn't sound like much but over a couple of hours it can add up to minutes) just by focusing on patient breathing and proper exhaling. I can only assume it will work the same for swimming once i'm able to get it dialed in.
And Nicodemus, i'm definitely not a coach, but skating drills seemed to help my weaker-side breathing.