Etiquette Question

I have a question for all you out on the internets. But first let me give you a ramble-y set up for this question.

I've got a religious bent. I think I've talked about this particular quirk before. I try to be respectful of what other people believe and their wishes. Above all else I wish not to offend anyone. So, here in lies the sticking point: I pray for myself and other people. I don't mean this in a get-down-on-my-knees-in-the-middle-of-lab way (but, at this point, I'm sorely tempted to give it a try), but at home, before bed, I do pray.

So, here's my question (it's long, I'm warning you). When something bad happens to someone my first instinct is to tell them that I'll keep them in my prayers. Should I do that? Is that rude? Because it occurs to me that it may be bad form. [What if someone is adamantly opposed to any religion? Or maybe that makes him/her feel that I'm imposing my beliefs on them? Or maybe someone just gets squicked out by the idea of someone praying for them? ] Maybe I should just stick with 'in my thoughts' or something similar. Any opinions?