With that in mind, here's a list of my favorite operas. I'm by no means an afficianado, but most of these operas are ones I've seen performed live or listened to over and over again on CD. Many thanks to malibran for gradually educating me to know what I like!
L'Elisir d'Amore (The Elixir of Love) - Gaetono Donizetti
I Capuleti e i Montecchi (The Capulets and the Montagues) - Vincenzo Bellini
Turandot - Giacomo Puccini
Les contes d'Hoffmann (The Tales of Hoffman) - Jacques Offenbach
Die Entführung aus dem Serail (The Escape from the Seraglio) - Wolfgang Amadeus Mozart
Die Zauberflöte (The Magic Flute) - Wolfgang Amadeus Mozart
I tend to like operas which are rather light, as opposed to ones that run three hours and suck out every ounce of your energy -- and patience.
Meanwhile I hope to add to this list as time goes on.