These are my favorite free apps that I have on my Android phone.
I think that most are available for Iphone also
AirDroid - connect phone to your computer wirelessly and move things back and forth. You actually see your phone content on the computer
Flipboard - choose what you want on your flipboard (here is example of some of the things on mine).. news, facebook,twitter,instagram,sports, women's health, Google+
Assistant - I love this app. You design your assistant and they talk to you. Your assistant will tell you jokes, make phone calls, add things to your calendar, find places on map, and so much more.
Gas Buddy - Find the lowest gas prices in your area or anywhere else.
News Republic - Alerts you with the top news.
Pocket - The pocket holds your favorite links for you in one place.
Endomondo - fitness app that tracks your walks/runs with GPS - works with Earndit site online where you earn points/ gifts for your fitness.
Nexercise - another fitness app that is part of a community. You can earn gift cards and other items by using this app