There aren't many complete opera recordings being made these days, but from the '50s (the beginning of the LP era) through the early '90s (the CD boom) there were plenty. One thing to note about opera recordings is that they have never really been an accurate representation of operatic history. For that, you need to go to live performances, in pirate and broadcast recordings, as many hard-core collectors do; I'm not very fond of these, myself, because they tend to be at best a souvenir of an evening. I tend to prefer studio opera recordings (now a dying breed) because, at their best, they can provide a satisfying dramatic experience in themselves, something that is separate from and different from the theatre experience. But anyway, many of the best operatic recordings have nothing to do with who was performing what in the theatre; for example, the famous De Sabata recording of Tosca, with Maria Callas as Tosca and Tito Gobbi as Scarpia, made those singers the classic heroine/villain team in this opera, but I think they'd never done this opera together onstage, and as far as I know they didn't appear together in Tosca until the '60s.
In the '50s and '60s, each company had their own "exclusive" artists who were featured in most recordings; Maria Callas and Elizabeth Schwartzkopf at EMI, for example, or Renata Tebaldi and later Joan Sutherland at Decca, or Zinka Milanov and then Leontyne Price at RCA. This meant that a lot of singers never got a chance to record their best parts, singers who were just as good as or better than some of the exclusively-signed artists (not that being less irritating than Elizabeth Schwartzkopf is a big recommendation). Still, this was, all things considered, the best era for complete opera recordings. The coming of LP and then stereo sound were perfect for opera, and the record companies made some effort at idiomatic casting: Italian singers for Italian opera, German singers for German opera, and so on. The Karajan recording of Verdi's Falstaff may have been recorded in London, but all but two or three of the singers were Italian.
By the '70s, the exclusivity system had broken down, but record companies became hyper-reluctant to take any casting risks, which meant that the same few singers wound up being featured in every recording by every company. Placido Domingo recorded Radames Aida at least four times, including three times in one ten-year period. In this era, there was little or no attempt at idiomatic casting, and most operas were recorded in London with non-operatic orchestras (the Philharmonia, the London Symphony, and the for-records only National Philharmonic) because it was cheaper that way. Because of all this, most opera recordings from the '70s, even good ones, have a cookie-cutter, bland feel, like everyone knows the music but doesn't really care much about what's supposed to be happening, dramatically. Conrad L. Osborne complained about this a lot in High Fidelity and James Levine, who conducted many opera recordings in the '70s, recalled:
When you record an opera in London, you have an excellent orchestra, but one that doesn't know the piece. You rehearse the 15 minutes you are going to record, and then you record it. After a while, I thought: This is the reason we have so many anonymous sounding recordings. However good the orchestra is, it's not the same as recording with an orchestra that you play opera with every day.
By the CD era, when companies started churning out dozens of opera recordings to meet what they (falsely) believed to be a huge demand for complete operas in digital sound, casting had become so haphazard that you couldn't even be assured of the anonymous competence of the '70s. The most infamous series of casting blunders was Deutsche Grammophon's insistence on casting their star soprano, Cheryl Studer, in nearly every opera recording they made, no matter what the opera; this resulted in one great recording, Salome, and a lot of disasters (Studer as Lucia, Studer as Violetta, Studer as Gilda). But lots of other recordings from this era suffer from casting that leave you wondering why X was chosen when so many other, better singers were available... and the only conclusion, usually, is that the better singers weren't famous enough or that the recording producers (who often didn't do a great job of keeping up with new talents) hadn't heard of them. One saving grace of this era is that more opera recordings started to be made with real opera orchestras (the Met Orchestra, the Vienna Philharmonic, the Dresden Staatkapelle) and idiomatic casting started to creep back in, as for instance Decca's all-Italian La Cenerentola with Cecilia Bartoli.
Now opera recordings, which are expensive to make and rarely make back their cost (especially since they're competing with all those great '50s and '60s recordings), have more or less been abandoned by the major labels, and the independents, which are otherwise doing a fine job of keeping classical recording alive, can't afford to make many complete operas. The future of opera recording is probably on DVD... but the patching-together of live performances onto a DVD can't be a true substitute for the pleasure of a good studio audio recording. Opera recording may not really represent operatic history, but it sure offers some solid entertainment.