How do you respond when someone says "Thank you for your service"?

It was an honor.

I say you are welcome; it was a privilege and a duty.

Sometimes I just say a simple thank you, but in reality it makes me uncomfortable because I only served in medical and intelligence, and the majority of my military time was during the cold war or mere combat support capacities.

I tell them "It was an honor and a pleasure" and then smile...

Always considered veterans Day for remembering those that didn't come home. So when you hear thank you, reply, remember the fallen...

"Thank you. It was my honor."

I just tell them "It was my pleasure" they seem to like it. :)

Thank you for your support!
That’s my usual response.
Initially, it seemed awkward to me that someone was interested or actually cared about my service. I was still in my teen years when I joined. I was just having fun.
I was barely learning the ropes on how to become a man -a soldier; someone with responsibilities. Over the years, I began to understand about my job and internalizing a military mind, military bearings, and the meaning of our motto: “honor -duty and country.”
Serving was and it congreatest honor. Although, We are not the only ones who sacrifice a great deal -family’s sacrifices with us. It’s in that vein where I truly welcome and humbly accept my fellows countrymen, women or children’s support, when they gratuitously offer a:
“Thank you for your service!”

I sometimes say I didn’t do much for for that.
I think “thank you for your sacrifices “ seems a bit more suited for combat vets.

I always say, "You're welcome". The declaration does not bother me. It also doesn't bother if no one says a thing. Sometimes I think we as veterans overthink things. I served 30 years USN active duty. 65-95. I went in because I wanted to, and I stayed because I liked it.