"And I shall talk to my dog for you. I expect similar results."

It depends on if I consider them important to me. If I don't, I just blow it off or thank them. If I do I usually say something about, while not following their beliefs, thank them and tell them that any positive thoughts, vibes or feelings are welcome.
Just as their "GOD" experiences do not influence me in any way, my knowledge will not influence them.

I remain silent or nod. If it is said in arrogance or superiority, I tell them I don't believe in prayer or their god but if they do want to do something for me join me working in the Community Center or garden. That almost always silences them.

I say "thank you",,,,all good thoughts are comforting, if nothing else, and I appreciate their kind thoughts for me......don't feel the need to respond with hostility to a kindly person.

I say thank you, as I consider the intent of acts, in this case kindness and support, more important than their efficiency.

If it's in response to my lack of belief , I walk away.

I simply say thank you.

Please don’t

I say.. don't waste your time.. I'm good. There have been a couple times when I am in a sarcastic mood.. I ask them why and to which god are you referring to? They just look at me kindof weird and really don't answer me back. It's kindof funny.

Thank you

Prayer is pretty useless, but it's not terribly offensive if they really think they're helping.

I tell them they are not praying for me and that they are praying for themselves because that is not something I want,it is something they want.

When my elderly mother, an evangelical atheist, was diagnosed with cancer, her former gardener, a Catholic, called her to wish her well and to say that he would pray for her. She told me later than she had to inform him that she did not believe in prayer because she is an atheist. I told her that the better response would have been to acknowledge his kindness and concern. Period. There is no need to preach at someone who is showing their concern by wanting to pray for you. It is called being gracious.

I say thank you because I assume good intentions and in that kind of situation I figure good intentions are good vibes being sent toward my problem whatever that may be.

A smile, a shrug and "Go ahead. It will make absolutely no difference".

Living in the UK, I get the impression that literalist, fundamentalist Christianity is much rarer than in the US. Over here, it is regarded as "a bit odd".

My most recent encounter - many years ago - was with a (then) work colleague, who sincerely believed in young-Earth Creationism.

After a civil but utterly unproductive exchange (me - Deep Time, radiometric and stratigraphic dating, the evidence for, and falsifiability of, Evolution - just one squirrel in a Jurassic bone-bed &c - the cosmic microwave background and the expansion of the Universe and more in the same vein, him - "The Bible says..." ) he popped the "I'll pray for you" line.

I responded that we were both fundamentally pondering the same questions... but that I seemed to need a better quality of answers. There and then we parted...

I used to say that I am a non believer but now just thank them as their intention is good,

I just say don't bother it wouldn't be worth it

Never been offered, but if so, I'd suggest they pray for themselves, since they need more than me.

It depends... If I am sick and feel like I am a few prayers short.... I'll just thank them. If they are praying for me because they hear me say that I am an Atheist... I just start laughing and say, "Good luck with that!"

My cat gets jealous when people pray to gods other than him so be careful...

I haven't even gotten that yet and I've been an atheist for 3 years now. I do stay out of religious conversations as much as possible and I never discuss it with family. But when that day comes, I will say "I'll think for you". That's the perfect response in my opinion.

Depends! If they say it in a snarky way, I tell them thanks, but no thanks, I will actually DO something to remedy the situation. If they are being genuine, I just say thanks, while rolling my eyes in my mind.

I usually don't respond but let it slide.

I say thanks for your consern and change the topic. I don't force my beliefs on others and hope they don't force their.

You must have too much time on your hands.