As it's often recommended on this forum, I thought I might post it as a separate thread:
From April until June, many of the most popular performances of the State Opera will be braodcast live on a giant video screen on the side of the opera house:
It's completely free and you can arrive and leave as you wish but note that all the seats are usually taken by opera-lovers before the beginning of the performance. So arrive early if you wish to have a seat to see the whole performance.
The complete schedule can be found here: