In this thread: lots of people that have no idea how to use siri, apparently.
I use siri to set timers (much faster than unlocking, getting to the clock app, selecting the timer tab, and scrolling through to set the timer) every day.
I use her to set calendar appointments. I use her to set reminders (often using relative dates (eg. 'siri, remind me in 3 weeks to give my puppies their flea medication')). Again, much faster than the tapping alternative.
I use siri to play tracks from various artists (I find this convenient when I'm driving. "siri, play panaphobia" -- she almost instantly identifies that it's a track from The Agonist and starts it).
And even though it's not the typical siri interface, the dictation interface uses the same engine and is quite good (it's seen some dramatic improvements over the last year).
I use her for lots of other things as well, but these were some of the things I can think of off the top of my head that I do constantly that don't fit into the realm of "all it does is search google; all it is is a directory; etc".
I'm not making any claims as to it's relative usefulness vis a vis cortana, but saying all it is is a directory/google lookup is flat out wrong.