From a fellow recent smartphone newbie (but Android, not Apple):
For currency converting, I love the XE app. You just tap the currency you want and it comes to the top, then you just shake the phone to reset it to 1 (so, if you were looking at euros to dollars, and now need to reverse it, you tap dollars and shake, and you get what $1 equals).
I just used Moovit for Israel (recommended by a local), which was handy for looking up bus lines by number, as well as routes. I see it has lots of cities and countries in its database, but haven't tried it yet for other places.
If your phone has a pedometer (my Samsung has this built in), it's fun to see just how much more you're walking in Europe than you normally do at home.
Facetime is great when communicating with other Apple users (already built in), but if you want to communicate similarly with non-Apple users, you may want Skype or one of its competitors.
See if the airports you are using have apps; they can be very handy with reminders, finding places in the airport, etc. You should also download the app for the airlines you are flying. For some flights, having the United app gets you free movies using the United inflight WiFi, but it must be installed before getting on the plane (tip from a flight attendant).
I agree that Rick Steves Audio Europe is great; once you've downloaded his tours, you don't need a data connection to use them. This app was just updated for iPhones (still waiting for the Android update).