I remember the first time I heard about quadratic reciprocity, I thought it was very "strange". If $p$ and $q$ are two odd primes, why is the question of whether or not $p$ is a quadratic residue mod $q$ related to the different question of whether or not $q$ is a quadratic residue mod $p$?
I remember reading some proofs and yet, not feeling that the proofs "explained" what was really going on under the hood (well, of course, they were proofs, and I did not have doubts about them, but they did not seem to explain the full story).
Then I was excited to learn about Artin's work and of course the Langlands program.
That being said, I remember watching an interview with Langlands where he remarked something along the lines that when he first learned about quadratic reciprocity, he just thought it was some kind of curiosity or something, but he didn't attach much importance to it (sorry for paraphrasing, if someone knows the exact quote, I can include it here, instead of my paraphrase!).