I am a catholic. I have taken the oath in court twice, once as a witness and once as a jury member. In both cases I affirmed. I believe that I should commit myself to telling the truth on my own honour/cognisances, call it what you will. I think that makes one think far more carefully about what one is doing than, in most cases, people doing what kittylester describes, just mumbling what to the person concerned is a mumbo jumbo mantra without meaning or religious impact. I do appreciate for some people swearing on a religious text does give weight and seriousness to their testimony, but I think they are now a minority.
As far as jurors are concerned, I took very little notice of what they said when they promised to tell the truth. All I was interested in was my judgement of the integrity and honesty of the witness they gave.