As predicted Google has launched a flight schedule search facility.
All you have to do is type in something like 'flights from Sydney to Los Angeles' and it will give you the flight schedule as results:
But it doesn't work for all searches. I tried 'flights Darwin to sydney' and got nothing.
I tried 'flights from' for a range of Australian capital cities, and mainly got what I expected, except for Darwin (no results) and Hobart - weird results below:
Apparently Hobart is also a place in Indiana, and its nearest airport is Chicago.
Obviously Google has a little more to do.