Apex Launcher
The best launcher for Android 4.0+. It's fast and it's customizable.
Smart App Protector
Allows you to require a password for certain apps and allows you to control the time of days it's required. For example locking down email, SMS, etc during the work day.
Allows you to keep the screen on when in certain apps. Better than Smart Stay since it works in the dark. Keeps the screen on for browsers, emails, forum apps, news apps, etc.
Allows you to block auto screen rotation for certain apps if you like keeping that feature on.
Widget Locker
Custom lock screens. Gives you a lot of options for customization.
Light Flow
Once it's updated. The developer has an AT&T S3 now and will update the app to properly control the LED in the US version.
PowerAmp
Best music player on the market. Using the ICS skin.
https://play.google.com/store/apps/details?id=com.ikorolkov.poweramp.skins.ics&hl=en
MX Video Player
Best video player
QuickPic
Much better than the stock gallery app
ES File Explorer
Best file browser. It's free and even has access to the root directory if you're rooted.
Go SMS Pro
My favorite SMS app. I like it better than Handcent. Using it with Smooth ICS skin.
https://play.google.com/store/apps/details?id=com.jb.gosms.pctheme.ssdsmoothICSblue&hl=en
Tasks
Syncs with Google Tasks. Looks and works great.
https://play.google.com/store/apps/...wsMSwxLDEsImNoLnRlYW10YXNrcy50YXNrcy5wYWlkIl0.
Genie Widget
The Jelly Bean version of the Genie Widget which is transparent. Looks great!
http://forum.xda-developers.com/showthread.php?t=1347792
Swype Beta
The best phone keyboard. I have Swiftkey 3 installed as well, but I never use it.
Lux
Must have auto brightness control app. It lets you go into the negatives (it applies a black filter to the display to make it look dimmer). AMOLED screens are too bright even on the lowest settings when you're in a completely dark environment like in your car at night or in a movie theater. This app lets you fine tune the brightness settings based on your preference.
https://play.google.com/store/apps/...t=W251bGwsMSwyLDEsImNvbS52aXRvLmx1eC5mcmVlIl0.