Not usually. But sometimes to Catherine, because she’s awesome.
I do all the time, ESPECIALLY to IT. I want IT to remember me as helpful, friendly, and cooperative. I don’t want them to pick up the phone when they have to call me and think “Oh god, not her”. I want them to call me when my number comes up, not delay because I am a pain in the ass who can’t right-click. And above all, I want to establish a strong relationship.
Same goes with anyone who I want to maintain a continued relationship with.
IT guys LOVE food. I cannot tell you how much good will you can generate with a plate of cupcakes.
They are 200 freakin miles away! I think even cupcakes would go bad in the mail. 
Bummer. Cookies work almost as well.
It’s candy for our IT guy and that will ship just fine (though he works twenty feet from me so that’s not a concern).
I’ve often thought about it but it does seem kind of kiss-ass to randomly send cookies. I think next time they solve a major problem I will send them something in thanks.
This. There is being polite, then there is Gaston and Alphonse.
And kiss ass is bad because. . .
I kiss ass all the time. It pays off in spades.
IT guys like having their asses kissed.
Ok, I think I will send them something. It’s summer anyway and we just finished up a huge event (our biggest of the year) so it wouldn’t be amiss to send a card saying “Thanks for everything this spring!”
I do this. Shamelessly. When I worked in the same office, I baked for them all the time. Now, one of them is an hour’s drive away, and the rest of them are halfway around the world, so I just grovel a lot. It’s not hard, because they actually are awesome!
As to the OP, it may depend quite a bit on your company culture, or the wishes of your client. I was on a client account in the last year (which I’m not involved with any longer, thank God) in which the principal contact was an incredible Nervous Nelly, and to maintain any sort of calm coming from his direction, we had to overcommunicate like crazy. We’d fix a problem, and he’d reply with “Glad that’s settled. Thanks.” and if we didn’t reply with, “Thanks!” or even just “Acknowledged.” he’d e-mail us a day later with, “Did you get my response? Just want to make sure we’ve closed that loop. I haven’t heard from you!!” I got to the point where I never, ever, ever received an e-mail from him that I didn’t acknowledge in some way. I acknowledged his automated vacation responses. “Thanks for letting us know! We’ll be sure to route questions to Shelly!”
I don’t do that to other people, though, or I’d probably be killed.
Me and a pal of mine have maintained an occasional “Thank you” “No, thank you!” email reply chain since about 2004. It started when he got me a very early Gmail invite. It’s like a bat-signal for us now, signifying “Pint soon?”
Apart from that, a simple “Thank you” ends the thing. If it’s a bit more than that, then another reply is possible.
I voted no but only because my reply would say “You’re welcome.”