I've got Apple, not iPhone, so not 100% sure whats out there. Must have is the SBB-App if you use trains. Its excellent and you can also get tickets through it. ZVV also has a good app.
GPS tracks exist for both Apple and Android and is downright brilliant. Free detailed topographic maps (the same you buy in paper in the store) for the entire country!
Search.ch or local.ch for your Phonebook needs, Quite reliable.
WetterAlarm is also really cool. At the moment only iOS but they are working on the Android version. You can subscribe for your region (home, work, preferred skiing etc) and then select what updates you wand. they then send you free push messages if there is a wind, raind snow, ice etc alert.
Swiss Tourism has a whole range of apps for iOS - i'm sure also some for Android. Some are very good, such as the Winter Apps, giving you an overview of the snow in all ski areas. Also some of the city guides can be very useful. They have a swim app for summer but I found that I tend to just jump in the Lake outside the house rather than look for a patch of water somewhere far away with my app.
There is a number of competing traffic apps. On iPhone, TCS (Toruing Club), SRF (Television/Radio), Swiss Traffic (ind.) and ViaMichelin all want to tell you where there is a traffic jam.
Most banks have apps telling you where to find ATM's. There are also some ATM apps which have all of them. I think local.ch can do that too.
SwissPost is good for looking up prices and opening hours. Migros and Coop also want to tell you when and where to shop. They also have their online shops via apps.
Starticket / Ticketcorner have apps to sell you tickets (and display then at the entrance) and I think sunrise, orange and swisscom now all have apps for you to see your current bill and data useage etc.
Havent checked with all of those whether they are also Android but more and more they will be.
Saving one of the coolest for last,
codecheck has a wicked app where you can scan any bardoce from products out of just about every supermarket and it will tell you what the ingredients are of the thing in your hands and if some of them will kill you, or have killed OrangUtans or Dophins and if they might give you cancer or whether African kids have been exploited for it. Very cool and the best way to drive your family mad at the sunday morning breakfast table and making sure that they won't eat half the stuff any longer thats in your kitchen. Have fun!