My favorite and most used app on Android isn't even an app, but rather a service. It is the Google Transit public transportation directions feature in Google maps, which can also be accessed more easily through the Maps application on Android - or on any other mobile platform which supports Google Maps for mobile.
In combination with the extremely dense and frequent network of public transportation in Switzerland, the transit directions on the phone offer a level of spontaneous mobility, which is generally associated with driving. When it came to using public transportation networks, people tended to know the routes by heart which they frequently travel (e.g. daily commute), while anything else required thorough planing by poring over books of printed time-table - an activity enjoyed only by the most hard-core train buffs.
The Swiss public transportation systems has always been particularly well integrated, across all providers and including everything from urban transit, buses, trains, boats to touristic mountain cable cars. The system-wide printed time-table the size of a phone-book has long been online and can be looked up at the SBB website. There is now also an Android app, Fahrplan CH - which acts as a query front-end to this site, but no official app yet as for the iPhone.
On the mobile maps application, finding next transit connections from the current locations is as easy as entering the destination, even a fuzzy one with some help from Google maps search & suggestions to find the exact destination address. The app shows the next few connections in an overview tab with total travel time and as a detailed list with connection times and description of each stop and carrier to take. A particular trip can also be viewed on the map, which is particularly useful for the first and last part which usually involves walking to and from the station or stop.
Unfortunate limitations of Google Transit is its model of treating each metro area in isolation, since the data usually comes from isolated transit authorities. Fortunately, Switzerland is represented as a single transit domain, but there is now way to display international directions - e.g. from a local address somewhere in Zürich to a local address somewhere Paris, which would involve taking a bus or tram to the main station, the TGV to Paris and a metro or bus connection towards the final destination. The SBB website does show basic international connection, but not at the level of every possible subway stop in every possible city, since that data-set really doesn't exist in a single integrated form.
Moving to a new city a few month ago, really was a good test for how well on-the-go transit routing and trip planing works. We didn't know our way around and often left the house only knowing where we wanted to go but not how to best get there or how to get back. But this only works in areas with very dense coverage of public transportation, where we can be sure that there is probably a connection every 15minutes or so and there will always be a way back when we want to and service does not suddenly stop in the middle of the afternoon.
It does not take a lot of imagination that mobility itself would be a killer application for mobile devices and dynamic public transportation routing in areas with good service coverage is clearly delivering on this promise.