I am an iPhone user. Here is why I like it for Stage Management:
Dropbox: It's an internet-based program, but has an iPhone app that allows you to view all your documents anywhere. It's nice because it doesn't require a lot of space on your memory.
Docs To Go: This is a purchase app that allows you to download and save documents in excel, word, and powerpoint on your phone, and edit them if necessary. I love it because you can basically have your whole prompt book on your phone, and editable.
Flashlight: obvious reasons.
Units: Allows me to have measurements anywhere-any and all units.
Yelp: Allows me to look up anything within my local area, and close by without crazy searches.
Map: Has directionality built in.
And basically the fact that it is a smart phone. I can get mail right to the minute about fittings, appointments, changes, etc. I also like how you can sync your calendar with Google Calendar, so that all your appointments and schedules are already on your phone...and it works both ways: if you put an appt. on your phone it puts it on google calendar.