(STILL UNDER CONSTRUCTION)
People have very extreme opinions of opera, either they love it and find it one of the greatest art forms to ever exist, or they hate it to death and mock it in every way possible.
But if you are curious about opera, there are things to consider: It is in fact the most elaborate of any live production: it involves acting, remembering all those lines, along WITH remembering all that music, which in fact very difficult. It takes years of training and practice to be able to sing that kind of music, act, and wear occasionally elaborate costumes under all those lights, straight from memory. Not to mention there are still all the other aspects of theater: stage direction, sets, costumes, lighting, the whole thing.
I'm not going to lie, there are a LOT of BAAAAAAAAAAD singers, these are the ones usually mocked. The vibrato can either make or break someone's sound. If it's too wide, the singer can lose the note they're supposed to center on, and some have been known to use that to their advantage because they can't find the right note. So when looking for performances and recordings, I'd suggest looking for their reviews before investing your money into sometimes very expensive works.
For starting to listen, you'll definitely want one of the more famous works and easy-to-follow works. Some are very complicated and many common and beginning people miss several amazing points. So here are some famous (sometimes considered cliche) works that are great to begin with, and from there I would suggest looking more into these composers and/or finding other operas like it.
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Giuseppe Verdi - "Rigoletto" (Drama) probably most-known for its tenor aria "La donna è mobile," it appears in so many commercials and TV and movies, most people don't know what he's saying, and are very surprised to find out too (here's a clip of Domingo with subtitles
http://www.youtube.com/watch?v=6HcrVzwlocA ) It's about a court jester who's found his long lost daughter, and the lecherous duke he's in service to has taken a liking to her beauty.
Giuseppe Verdi - "Aida" (Drama) One of the most commonly-performed operas to this date, this is a romance that takes place in ancient times of an Egyptian war hero (in the war with Ethiopia) falling in love with one of the princess's slaves, Aida. Leontyne Price singing the main soprano aria, "O patria mia"
http://www.youtube.com/watch?v=W6kR5ZvLN80W. A. Mozart - "Die Zauberflote" (The Magic Flute) (Comedy) A Singsphiel ("Sing-play," a comic show with both spoken and musical parts). This fun show has a role for nearly every voice type, from a coloratura soprano to a dramatic bass. There are virtuoso parts, and amature parts, and child parts too. There are several styles in this show as well, almost like a grab-bag for styles from a baroque choral, popular folk-style, and sophisticated grand opera. The story is about a prince and his quest for love, with the help of his new friend Papageno the bird caller.
"Der Hölle Rache" (The Queen of the Night's most famous aria) performed by Diana Damrau,
http://www.youtube.com/watch?v=DvuKxL4LOqc and Malti Salminen singing "In diesen heil'gen Hallen"
http://www.youtube.com/watch?v=EdRaAtfgMd8W. A. Mozart - "Don Giovanni" (Comic Drama) Musicologists still try to classify this between drama vs. comedy but Mozart and the librettist da Ponte called it a Drama Giacosso (comic drama). It is both hilarious and horrifying, an interpretation of the very unfunny legend of Don Juan retold in a more light-hearted way. There are both hilarious moments, such as Leporello's famous "catalog aria" describing all the women Don Giovanni has dominated
http://www.youtube.com/watch?v=l0lN6SJkpBQ sung by Furlanetto. And also very dramatic and heart-filled, with one of Mozart's most adored arias, "Non mi dir"(sung by Rene Flemming, same performance as the other clip)
http://www.youtube.com/watch?v=yrTgxcI305kRichard Wagner - "Lohengrin" (Drama) Wagner is musically controversial, from people who love his music, to those who HATE his music. Personally I think his music is gorgeous, but idiotic in that it is so physically demanding it is hard to find an enjoyable performance because of how much is cut, or because it's so easy to mess up. Of all his operas, Lohengrin is probably the easiest to follow with several reacurring themes. It is very long but not as long as his other shows. I'd suggest not listening to this until listening to a few other operas first because of its length. This is a fairy-tail-like story of a woman rescued by a magic knight who reappears in a boat carried by a swan. Most people know its bridal chorus from act III as "Here Comes The Bride" though the true words are much different, but three times more lovely (Wagner wrote his own librettos which I do find beautifully done).
http://www.youtube.com/watch?v=8J7Jhx93s9w for bridal chorus, the overture:
http://www.youtube.com/watch?v=7prUFflX0_E and the finale (if you want the story spoiled, it is a beautiful excerpt)
http://www.youtube.com/watch?v=8U8_3OxCJ8w