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

I say the same, because without there support while we are serving our nation, things might fall apart. To me there is never just 1 its always 2 or more that make it happen. I severed while my friends that couldn't serve kept our Nation strong with there being here running things.

I say thank you and move on.

So, this question has so many answers depending on the nub that is asked it. I joined on 6-month cache in 1972, went active in April 73 to boot. 3 days after my enlistment Nixon came on the tube and said, "we all done there" and off I went to boot. I finished high school mid-term cuz I was so smart and after boot went back to my HS in my shiny new blues to stud about. A former buddy saw me strutting about proudly in my spanking new uniform and called me a baby killer and then spit on my shiny new shoes. The resulting discussion did not enhance our friendship and resulted in certain biological enhancements to the color of his face...
About 1991 or so at the beginning of Desert Storm (the first one) I had to go into town for of all things, a case of Loctite for the ship. Setting in my car at a stop light in my khakis, piss cutter on my scull, ribbons on my chest and waiting for the light to turn green, a random civilian crossing the street spies me through the windshield, pops tall and throws me a salute! Suddenly I'm a fricking hero! Well how bout that?
Over the years I hear this "thank you for your service stuff" all the time, sometimes from people my age and I appreciate it, and often from some kid with zits and a vapid stare at McDucks or something cuz the Boss said say it.... I am thankful for the former and I blow off the latter cuz they don't know and I can't explain.
What does this saying actually mean? Well from some folks it means a lot and I feel gratitude but a bit embarrassed, I didn't die, I served in a hole of an amphib most of my career and never dodged anything but a wrench from some frustrated non-rate... but I did the job and I did it to the best of my ability and I generally did it right - and I am and was damn proud to serve! So, I say I was proud to do my duty.
For the gum chewers and ain't got a cluers... Whatever "you're welcome" because why be rude?
But how you answer the question and how you feel about it is up to you. For you youngsters who started your career about the time of 9/11 and are used to being regarded as heroes, I'm glad for you, for us Viet Nam/End of Nam guys, the experience has been different.
Regardless... I give you a heartfelt "THANK YOU ALL FOR YOUR SERVICE" you have done and are doing well!

Quite some time ago this subject was brought up on a FB group, Disgruntled Underground 2.0 and one response said they respond with "You were worth it".
I tried this a couple of times and it made the person ponder exactly what they are thankful for.

SP5 Sonye when I wear my Cold War veteran cap with unit pins I say thank you and answer any questions they have

SP5 Sonye when I my old war veteran cap with unit pins I thank them and answer any questions they may have

I thank them for their support.

You were worth it !!! that usually floors them seven more.

Update: veterans can have their veteran status noted on their drivers' licenses. Not sure about active duty.

Thank you for your support and I would do it again!