Hmm... let's see... OK, I got it: I can agree with all of them, in the exact same order.
Thanks for taking my top 10 as the initial suggestion. Please allow me to defend my choice a little bit.
First of all, we need to try and define why we consider some operas to be the greatest. I guess it has to do with a number of characteristics, more or less weighty depending on individual values. But beauty in my opinion should definitely be one of them. Of course beauty is in the eyes (or ears) of the beholder, and while some people find extreme beauty in melodious Bel Canto or Baroque, others can't stand the sound of a harpsichord and find beauty in dissonant/atonal works. Nevertheless, how can we ever avoid the "beauty" part in such selections?
Innovation should also be a consideration. Operas that belong to a certain movement or era and don't really do much to advance the artform have their place as well - they may derive their place from the "beauty" part - but there is something to be said for those that are divisors of waters... think of Monteverdi as one of the pionners, of Gluck changing the ways of opera seria, of Mozart's spectacular orchestration, of Verdi evolving from aria numbers to scenes to through composition, of Wagner introducing musical dramas and shifting the direction of music in Tristan & Isolde, of R. Strauss oscilating between tradition and modernism, of the New Vienna School again turning music into a new direction, etc.
Lasting popularity is another consideration. What is popular is not always equal to what is good - McDonald's is popular but I'd still prefer a gourmet restaurant anytime I can afford one - but again, there is something to be said for lasting popularity, in the fact that such operas are not just a product of time-limited fashion but endure because they reach some sort of truth or some sort of expressive connectivity with the audience that make them be heard over and over. In other words, these operas have passed the test of time.
Cultural identity is another one - and one thinks of what can be said to be authentic Russian opera, Italian opera, German/Austrian opera, French opera, etc. Certainly we're bond to select in the list of 100, operas that are not widely known but are vigorous regional examples that aren't better diffused thanks to language barriers, niche admirers, etc - which doesn't mean they aren't good enough to be included.
Libretti are also important. Great music has been set to rather ridiculous plots, and some operas survive their bad libretti, but it does help when libretti are top quality as well - which relates to the literary value of the source, the poetry of the librettist, the talent in dealing with this special medium in which it takes a lot longer to tell a story because the story is being sung rather than spoken. A Boito, a Da Ponte certainly add to operas and may raise their final rankings in our lists.
Many will probably suggest very obscure operas. I don't doubt they may be very good, but I'd like strong evidence that they belong in a list of 100 greatest rather than in one of interesting works to be explored, but that don't quite exhibit all the qualities necessary to belong in such a list. I'm afraid of a certain fascination for the obscure or the new, before these works really and truly prove their mettle. It's like certain food critics who quote small restaurants and grant them some grade inflation, as opposed to those of celebrated chefs. I think a certain consensus is important in a list like this. There are many fine operas out there that aren't known to the wide public but to say that they are among the 100 greatest in my humble opinion would be stretching it a little, for the lack of this consensual quality. Anyway, that's just my opinion, others may feel radically differently about this, and that's why this thread may become interesting because I'd love to read arguments pro and con the inclusion of some operas. At the very least, this will make us more familiar with more obscure works.
So, let's see my initial suggestion, how do I defend these ten?
1. The Ring of the Nibelung - for its scope and ambition and long-reaching arc and its sublime moments, in spite of some longueurs.
2. Les Troyens - one of the most underrated operas ever, a sublime masterpiece with a sense of History and the everlasting battle between love and duty, coupled with astounding music, including phenomenal chorus music, in a tight packet in which nothing is superfluous or unnecessary in spite of its length.
3. Tristan und Isolde - for the sheer beauty of its score and scenes, and the lasting impact on Western music of its innovative approach
4. The Marriage of Figaro - For the brilliance of the orchestration, spectacular pace, large number of outstanding arias, exquisite libretto
5. Otello - for the psychological depth, impactuous defining moment, powerful written through composition, outstanding libretto
6. La Boheme - for the romanticism, soaring melody, touching moments, and general addressing of the question of youthful passions and life in the moment
7. Don Giovanni - for being so wickedly entertaining and tracing so well the arc between light humor and serious drama from beginning to end, as well as the same above mentioned orchestration and libretto qualities of the pair Mozart-Da Ponte
8. Die Meistersinger von Nurnberg - for one of the most extraordinary characters in all of opera (Hans Sachs), for the love of music expressed in it both in musical and dramatic terms
9. Norma - Casta Diva. Enough said. That's maybe the peak of beauty in all of opera.
10. La Traviata - OK, this one I believe will be controversial to include as high as top ten, but I stick to my guns here. Lasting popularity is a given, but it's not all. It's also the evolution to scenes rather than arias, the precision of its musical construction (the first act is a thing of beauty in its precise tone panting, the Germont-Violetta scene with its subtle psychological progression fully expressed in the music is another one), the profound shift in tematic, bringing in regular people with regular psychological issues rather than historical or mythological subjects, and lets not forget the beauty of its arias and overture/intermezzo.
I'm looking forward to hearing about other people's top ten and why they list them in there.