Is it common/correct to say "thanks for having me" after an interviewer says to you "thank you for coming to this interview"?
Update: I'm referring to a job interview. (Thanks for pointing that out)
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I would say "Thank you for this interview" but more importantly, the interviewer may have seen a dozen people in a short time, and recalling your specific attributes may be lost without the post-interview thank-you note. A handwritten, plain note-card, posted (never emailed) is a tactile action that once again puts the focus on your candidacy.
In the UK "thanks for having me" would most usually be heard from a (polite) child thanking a friend's parents for a meal etc. A more appropriate phrase after a job interview might be something along the lines of "Thank you for your time", "Thank you for taking the time to see me" etc.
As an employer (again in the UK - I can't speak for elsewhere) I'd certainly recommend a follow-up letter (or maybe email if its that kind of business, NOT EVER a postcard) thanking your prospective employer and (if you can think of something appropriate) following up some point raised in the interview. It will remind them who you are and will prove you can write!