One of these days someone was telling me that theater goers who are used to high quality stage plays with good dramatic impact and high literary value are turned off by opera because most operas have silly plots that badly fail as plays. Of course the point of opera is primarily the music, but as someone passionate about the genre, I would like to think of which operas hold their own in terms of dramatic impact and theatrical value, and can be compared in terms of these elements to the best stage plays, independently of the music.
While this is less true of opera buffa, some are good comedies in my opinion. I'd quote Il barbiere di Siviglia and Le Nozze di Figaro as good comedies, as well as Gianni Schicchi, L'Heure Espagnole, La Pietra del Paragone, Don Pasquale, and L'Italiana in Algeri. Some others are excellent musically and very entertaining (like L'Elisir d'Amore, La Fille du Regiment, etc) but I'm not listing them because without the music they wouldn't be as funny as simply stage plays, in my opinion.
In opera seria, semi-seria, and especially modernist and contemporary opera, we find numerous ones that could perfectly work as stage plays even without the music (of course, many of them do come directly from plays).
A non-inclusive list: Pelléas et Mélissande, Peter Grimes, The Rake's Progress, Porgy and Bess, The Dialogue des Carmelites, Moses und Aron, Oedipe, The Turn of the Screw, Lady Macbeth of Mtsensk District, The Minotaur, Lulu, Wozzeck, From the House of the Dead, Janufa, Die Frau Ohne Schatten, Elektra, Salome, Thaïs, Il Tabarro, I Pagliacci, The Queen of Spades, Eugene Onegin, Carmen, Les Comtes d'Hoffmann, Tristan und Isolde, Tannhäuser (I'm not sure if other Wagner operas would work as theater without the music), Falstaff, Otello, Don Carlo, La Traviata, Rigoletto (but not Il Trovatore), Macbeth (but not Ernani), Norma, Lucia di Lammermoor, Lucrezia Borgia, Roberto Devereux, Maria Stuarda, Les Troyens, La Damnation de Faust, Benvenuto Cellini, La Clemenza di Tito, Don Giovanni, Hercules, Orlando, Giulio Cesare, Dido and Aeneas, The Fairy Queen, Orphée et Eurydice, L'Orfeo, L'Incoronazione di Poppea.