It's certainly a matter of personal style, and it's most important to be yourself. I love playing with the camera, i'll stick my shoe in there or smile right into it (it depends a bit on the style you play, too. I might not do that at a jazz gig, but I will at a Rock gig). it's not doing anything differently, I just have fun, and since I love what I do it's easy to smile. Communication with the audience is a big part of the show to me and a camera obviously communicates back in a way that can create a bit of back and forth. People love to watch that interplay as well.
I used to be camera-shy, stage shy, everything. i used to think I wont be taken seriously as a musician if I contribute to the 'show' part of things. At some point music just got so strong in me and swept me off my feet and none of these things mattered anymore. It was a big relief and helped me be more authentic on stage.
I study photos of myself a good deal also for another reason: I don't mind looking goofy, but if my students get to point out that my finger position (or whatever) is not like I teach it to them, then I need to look at this. In the heat of the moment hidden bad habits can show. I also truly view adequate showmanship as part of my job and the camera provides the best feedback there is.
Great pix sent to us by fans has a great value (nothing like a good live shot), so I make sure I give the photographers due credit and ask permission to use etc.
Anyways, say cheese.... or not... but dont let anything take the fun away.
Ariane