I recently saw a comedy improvisation show by Colin Mochrie and Brad Sherwood (from Whose Line Is It Anyway) at the Opera House as part of the Just for Laughs Festival. Definitely my favourite thing I've seen there so far, even though it was in one of the smaller theatres there. My husband and I laughed so much we had tears running down our faces. Doesn't get much better than that!
The Opera of course! One of the best operas I've seen was Puccini's La Boheme. Beautiful production and great use of the stage with regards to scenery and set design. It feels grand an intimate at the same time.
Some fantastic bands and musicians have had some great shows at the Opera House: Grizzly Bear, Antony and the Johnsons and Bon Iver to name a few (all put on amazing shows, made good use of the space's acoustics and provided gorgeous visual accompaniments). Everything that goes on during Vivid Sydney is always a treat - particularly the Opera House's spectacular light projections.