I always liked the idea of declarative programming, it felt very natural when I first learned about it. That being said, I didn't have much use for Prolog after finishing that class. (I wrote one fairly small application at my first job, but really nothing else).
I think that if you're interested by any of the recent developments around the Kanrens (or Core.Logic if you're a Clojure programmer), you'll find yourself better served by at least having a passing familiarity with Prolog.
I also find that SQL feels to me quite a bit like Prolog (you have to sort of squint), and I find myself liking writing SQL way more than you're apparently supposed to from how much people complain about it online. That might have nothing to do with having learned Prolog, maybe my brain is just wired wrong.