A lot of composers that write in the classical style are doing movie soundtracks now. I know it might seem pedestrian compared to Mozart, but maybe the way to look at it is movies are the modern incarnation of opera. And there are some mighty fine soundtracks out there:
Best Soundtracks - ALL-TIME 100 movies - TIME
Still, the classical stage isn't empty yet. There are new classical pieces being written. I know he's very controversial, but Philip Glass is a particular favorite of mine (so long as I don't listen to it too often). I also really like Christopher Rouse. He actually has a myspace, believe it or not:
Christopher Rouse on MySpace Music - Free Streaming MP3s, Pictures & Music Downloads