The most recent experience for me was my Grandfather's funeral. I am an atheist, but wanted to join the ceremony to mark his life, which was a Christian event. I chose the middle course of attending but not participating in prayers. To me, prayers are "just words", in that they have cultural symbolism but no personal meaning thus I could have participated, but felt it might be seen as devaluing the belief of others. Another attitude, expressed by some teachers at my school, was that one should participate regardless of belief, because the event was a Christian service and if one was at a Christian service then there were certain things that should be said.
(FWIW, for me the hymns were different to the prayers, I was happy to sing along (as much as I ever really sing) and would have felt more awkward staying silent then.)