I got a Galaxy Nexus not long ago. Nice phone. I was actually debating between the S3 and the Nexus. They're very similar apart from a few details.
It was an upgrade from a Samsung Intercept. The difference is tremendous. I love it.
As for apps, I use:
Accupedo - Pedometer
Astrid Tasks - Task management
Chrome - Web browser
eBuddy - Chat
Gauge Battery - Nice battery widget
Light Flow - Custom LED notifications
Netflix - Well, Netflix!
Pandora - Streaming music
SMS Backup & Restore - Archiving text messages so they aren't slowing down your messaging app but you still have a history
SMS Popup - Pops up text messages even when your phone is "asleep"
SwiftKey - Awesome replacement keyboard, much better than the original (unless you have Swype, that might be better)
Widget Locker - Better lock screen (worth the $3.99 or whatever it is)
I also have some nice games on here.