I used to think it was the aria "Un bel di vendremo" in Puccini's "Madama Butterfly." Here's a short video where you get a bit of the song in the glorious Metropolitan Opera's production---starting at the 1-minute mark. I saw this production on PBS once and cried most of the way through, And check out the interview with the amazing singer toward the end.
But now I realize it's "Una Furtiva Lagrima," from Act II, Scene 3, of "L'elisir d'amore," by Gaetano Donizetti. According to Wikipedia, "It is sung by Nemorino (tenor) when he finds that the love potion he bought to win the heart of his dream lady, Adina, works. Nemorino is in love with Adina, but she is not interested in a relationship with an innocent, rustic man. To win her heart, Nemorino buys a love potion with all the money he has in his pocket. That love potion is actually a cheap red wine sold by a traveling quack doctor, but when he sees Adina weeping, he knows that she has fallen in love iwth him, and he is sure that the 'elixir' has worked."
Here is this aria or romanza as sung by Luciano Pavarotti. Check it out. And go back to the Wikipedia page to find the words in Italian, a literal translation, and a "poetic translation."
Wait, here's a better version, I think, sung by Matthew Polenzani. And this version has the English words on the screen, a different translation than in the Pavarotti version. And, what's even better, Mr. Polenzani is actually acting the part of Nemorino, instead of acting the part of a famous opera star. Also, I loved scrolling down and reading the comments by the opera aficionados.
Wait, I'm changing my mind again, listening to "Un bel di" over and over again. Now I think this is the best song ever. Here's Maria Callas singing it.