Believe it or not, opera used to be popular music once. The people in the older days had the same need to have fun and to enjoy themselves at musical events as we do now (yes, yes, even your parents were kids once, too!), and it follows that the music of the opera isn't really all that boring and unengaging as some who haven't themselves given the genre a good try would have you believe.
The problem with deciding whether you like opera or not, I think, has a lot to do with whether you have tried enough of its variations. This is a big fat classical music genre that really has something for everyone. Here are a few tips I'd give to those who aren't familiar with the opera but would like to give it a try:
1. Try many different styles of opera right off the bat. It doesn't do to say that one doesn't like opera after having heard only 2 or 3 works of the same sub-genre. How diverse is this music theater genre? Go through these clips and see/hear:
Renaisance Opera - Monteverdi's Il ritorno d'Ulisse in patria (The Return of Ulysses to His Homeland), Landi's Il sant' Alessio.
Baroque Opera - Handel's Alcina, Handel's Ariodante, Broschi's Idaspe
Classical - Bel Canto Opera - Mozart's Apollo et Hyacinthus, Mozart's Don Giovanni, Mozart's Le nozze di Figaro, Rossini's Il barbiere di Siviglia (The Barber of Seville), Bellini's Norma, Donizetti's Lucia di Lammermoor, Bellini's I Capuleti e i Montecchi
French Grand Opera - Meyerbeer's L'Africaine, Saint-Saens' Samson et Dalila, Delibes' Lakmé
French Opera - Gounod's Romeo et Juliette, Gounod's Sapho, Massenet's Werther
German Opera - Weber's Der Freischuetz, Wagner's Tristan und Isolde, R Strauss' Der Rosenkavalier, R Strauss' Elektra
Slavic Opera - Mussorgsky's Boris Godunov, Tchaikovsky's Pique Dame (Queen of Spade), Janacek's Jenufa
Italian Opera - Mascagni's Cavalleria Rusticana (Rustic Chivalry), Verdi's Don Carlo, Puccini's La Boheme, Puccini's Madama Butterfly
Operetta - J Strauss' Die Fledermaus, Lehar's Die Lustige Witwe (The Merry Widow), Offenbach's La belle Helene
Modern Opera - Berg's Lulu, Adamo's Little Women, Britten's Billy Budd, Copland's The Tender Land, Tan Dun's Tea, Glass' Einstein on the Beach, Adams' Dr. Atomic
2. Listen to 'live' recordings whenever possible rather than the studio recorded ones. You see, many people develop unrealistic expectations of their opera experience from listening to studio recording too exclusively and losing touch with how difficult it is to sing these music to the live orchestral accompaniment while acting... without the benefit of re-takes and sound engineering help. Studio recordings can be taken as the ideal that such and such performer can execute the music under maximum control condition. Studio recording sessions see the singer recording each aria (song) in fragments rather than the whole way through. They don't have to compete with the orchestra volume (so beware of judging a voice size from just these recordings. A sound engineer can make an ant sounds like an elephant with a turn of his instrumental knob!).
The trade off, in return for super clean musical execution, is that studio recordings generally sound less emotionally and dramatically involved than its live counterparts do. It is hard for a singer to carry a coherent dramatic message when the scene is recreated in fragments, with the producer getting to splice the various takes in creating the final version... All in pursuit of the most beautiful sound achievable. So, it is just as unrealistic to expect a totally clean execution in live recordings as it is to expect gripping dramatic tension in studio recorded ones.
3. Go to live performance as much as possible. As good as these singers sound on recordings and at HD broadcast to movie theaters, there is nothing that can match hearing and seeing them live on the stage... without any acoustic distortion from the recording process! And the orchestra! And the ballet dancers! When you go for the first time, though, avoid orchestra level (the expensive seating) and go for the front of the balconies instead. While it is true that sitting in the pricey orchestra level or even the dress circle can be perceived by others as a sign of your financial affluence, the sound quality there tend to be awful. With the aid of a good opera glass (binocular), which may or may not be needed, you can catch the best of both worlds (visual and acoustic) of the performance from the front center balcony for a good price!
4. Don't let the opera snobs dictate what you can or cannot like. As 'refined' as the image of this artform is, you may be surprised to find that some of its audience can turn out to be the most sophisticately barbaric people you'll ever meet. Most opera fans are nice lots, mind you, but the most vocal among us tend to be little Napoleons who won't hesitate to tell a doctor how to operate or a mechanic how to fix the car... and they sure don't mind telling you just how awful a performance you enjoy really is. Take it from me, opera is for everyone and not just a bunch of self-proclaimed music scholars who are so involved in their superiority complex that they would declare a fine performance ruined by a single smudged note that saner people would have the good sense to not get hung up on in the first place. You paid your own money to hear the music, too. As long as you aren't trying to convince others that your preference is the only acceptable one, they have no right to try to do such a thing to you.
5. Keep trying the operas that you don't like at first periodically. Opera can grow on you. There are some works that are so musically complex that it takes a bit of listening experience to come around to appreciating. If you try something and don't like it, go and listen to something else for a while... but do come back later (a day, a week, a month, a year, a few years... it doesn't matter) and give it another shot.
Sometimes it takes a different interpretative approach to make the opera 'click' for you. So do try different performances of an opera by different performers. Who knows, maybe you'll find that you like many different artists (this is a good thing! The art isn't a competition, but something that should widen your perception when you learn to appreciate its variety) rather than just one.
And last of all... Have fun! It's entertainment and not an art-appreciation class. The performers and the other audiences are just people like you are. They breathe the same air, eat food (and excrete it... there are restrooms at the opera house after all), get sick, get tired, and have feelings just like you do. Heck, I've even heard a soprano sneeze once... Don't expect perfection out of them. Expect humanity!