I have an iPhone 4s so here are the apps that are my favorite and all are located in the App Store. I will not feature Facebook or Twitter within my post because I think everybody already has those apps. I'll provide the link to each app so you can read up all about the app and its features.
Sports
Scorecenter: This is a free app that allows you to add your favorite teams which will give you easy access to scores, stats, etc.
Official Husker app: This is also a free app that you can news feeds from all the athletic sports that Nebraska provides. Its also great listening to the live feeds from any event which you can pay all sports live streams with one easy purchase or choose which sport to listen too. I only pay for the live feeds for baseball. Very great app for any die hard Husker fan
ESPN College Football app: Free app that gives you news feed, scores, videos, recruiting. You can also add your favorite school and from there you can read up on the news about your school, see scores, recruiting, videos, etc. Love this app around football time.
BTN2GO: This app is also free and just like the Husker app it to provides stats and scores from any B1G school and you can select your favorite team. This app also allows you to watch any program that is currently live on the Big Ten channel but you can only watch these live feeds if your cable/satellite are available within the app requirements. I've only watched a few games using the app when my TV was already occupied.
Tunein Radio: This app is also free and I have found a radio station that does air the Husker Football games and I've used it a couple of times to listen to the post game shows. You can also listen to other radio stations that play music or listen to a police scanner for certain cities around the US.
Camera
Instagram: This is also a free app and I use this app constantly. You create a free profile and what you do is you can take a picture of anything and edit the filters of that picture and post it. In the description of your photo by adding hashtags allows other people to view your photo and like and/or comment on that video. Instagram just added a new feature where you can record videos and post it as well.
Camera+: This is also a free app that allows you to edit your pictures just like Instagram. I mainly use this app to take photos of myself and my son using the self timer feature of this app. I'm not a fan of the front camera cause I want the best crisp photos using the 8mp rear camera and this app does the job with the self timer.
Color Splash: This free app allows you to edit your photos from your camera roll. You just simply upload a photo and you can color certain parts of your photo and leave the other parts of your photo in black and white. Really cool editing app
Movies
Flixster: A free movie app that allows you to look up movies and see what kind of ratings it got. You can watch movie trailers or see what times the movies are playing in your location. I use this all the time since I'm a huge movie buff. I have The Dark Knight rises on my profile on Flixster so I can watch TDKR anywhere I want to which is also nice
Weather
The Weather Channel: Free app that allows you to see what the weather will be like for that day or what the weather will be like for the whole week. You can also check out the weather on the radar that'll show you what the weather will look like with a two hour outlook I believe. I use this daily to see if its nice out to ride my motorcycle to work or not
Music
Soundhound: This is a free app that allows you to discover that new tune thats playing on the radio that you like. I love this app and use it quite frequently. If your at a restaurant, driving in your car or at the club and you hear a tune you like just open the app and click on the Soundhound button and it'll find you the artist and the song title. It will also allow you to purchase that song through iTunes.
Games:
PSN friends: This is a free app that allows me to see who's logged onto their Playstation 3. I use this a lot cause if I'm curious to see whos on I'll open up the app and it'll show me which friends are on and what games they are playing. I use it quite often so I know when to get online to play with my buddies.