I usually just tell them I'm thinking of them, and if they need anything to let me know. And then, you know, actually do it if requested. Unlike praying, which does nothing.

I usually say, "My heart is with you."

I just usually ask if there is anything else I can do for them.

It depends on my relationship to that person and the situation they face. Still, if someone is really hurting, or facing loss or real misfortune, I’m certainly not going to respond with some pissy rebuke of their theology or choice of metaphor. If it’s something I can tangibly help out with, I’ll consider offering. If it’s more a matter of expressing sympathy or consolation, I’ll do that with phrases I’m comfortable with, like “sending my love,” “wishing them the best,” or any of hundreds of ways one can express care and concern.

I say "sending science your way", instead of prayers.

I also don't believe in luck so I just say "well wishes and safe travels"

Prayers doesn't do anything. Try something tangible like donating for medical bills, be present, bring their favorite meal, etc. Anything that can actually alleviate the pain, depression, etc.

Something like "I'm always pulling for you, hang in there."

Whoever called for the prayer, I bring over the blackest goat with the biggest, gnarliest horns, start a large fire, take my clothes off, sacrifice the goat to the dark lord, engage in the ritual dance of darkness and smear the blood of the goat all over myself. It usually helps!

I usually say keeping good thoughts.

I deal with this all the time. My advice is do not reply the way I do unless you think they won't be offered. I say I'll do better I'll help if I can. You can shorten that to be less offensive to, what can I do to help you? If it's someone I don't know or care about say pray for me, I say my prayers don't work what can I personally do for you?

I hate that situation. I always tell people I am thinking of them and ask if there is any actual real thing I can do to help. My real friends and family all know I am an atheist so I don’t ever get asked for prayers and they understand my response. Since I avoid most social media like fb I rarely have to deal with this anymore ??

My thoughts are with you....that’s my go to response

My thoughts are with you. What can I do to help?

My heart is with you and your family...

If it's a close friend or family I wouldn't hesitate at all to join them in what ever it was they wanted to get through a hard time. It wouldn't mean I am buying into it but just being the person they need.

"My thoughts are with you and your family pal. If you need a chat and/or a beer, give me a buzz and ill be there. Stay strong."
Unfortunately this is the short version of what I sent to my best mate of 30 years this morning as it seems his mother is at the losing end of her battle with cancer.
Says it all really... thinking of you, here if you need me, good luck.

I say some variation of thinking of you

I wish you well. Yes, it's as simple as that.

I wish you well.

You're in my thoughts and heart.

I always say "I'm thinking of you".

I typically act as if I didn’t even hear it and move on

Best on you always.

Similar to the rest. You are in my thoughts.