Yes, it is imperative that you breathe while playing guitar. In fact, no activity should be attempted without breathing ?
No but more seriously, I have heard an interesting and convincing argument being made for breathing as if you're singing. The point was that you should try to imitate a voice with your guitar playing and if you breath as if you're singing, you will develop a more natural feel for where the phrases end etc.
It's very academic and I doubt you'd find a video that illustrates how breathing correctly makes the music sound better than breathing incorrectly but there is a certain amount of logic in the argument for me.
I very much like the notion of trying to imitate a voice with the guitar (and I'm horrible at it). But if I look at the guitar players that really inspire me (Gary Moore, Peter Green, Mark Knopfler) their playing seems to be much less about maniacally racing over as many notes as possible in as little time as possible and more about imparting a "feeling" in their solos. The best description I've heard is that they use the guitar like a voice.
Here's an interesting write-up that mentions this approach to breathing correctly while playing.
http://www.classicalguitar.org/2009/03/breathing-while-playing-guitar/