Welcome to Android! You made the best choice, Galaxy Nexus with ICS 4.0 is the best smartphone experience out right now. I love my Nexus for the staggering amount of customization options. Of course rooting your phone allows even further customization/control.
Stock ICS is great, no doubt. Rooted however is just frikking awesome!! If you have any interest in root I can point you in the direction of some apps that make your phone truly powerful. If not there are still some other ways to make your phone awesome.
Rooted apps:
Titanium Backup.. essential for backing up everything, apps, contacts, settings. I've even used this to save everything and transfer it all to a second device. Amazing
Light Flow.. Gnex has an awesome LED notification light but it doesn't work that great without this app. With it, you control which colors are for each different notification, how long it flashes for, frequency of flash etc. I even set specific colors for individual contacts. If I see a fast flashing purple light I know it was my wife before I even pick up my phone. Much needed app.
Set CPU.. Control cpu clock speed in different modes. I don't need my cpu running at full blast while in sleep mode in my pocket eating up my battery. Trust me the Gnex battery gets eaten up fast with that beautiful huge screen and 4g radio. I use this app to slow down the clock speed when not needed. Essential.
Ad Free.. Simply removes ads from your browsing experience and even blocks them in free version apps.
Juice Defender.. Another battery saver. This one turns off battery draining 4g and 3g radios while in sleep mode.
Quick Boot.. Quickly reboots your phone into several boot modes. Handy for not having to take your case off or battery out if you ever have to reboot. Other uses as well for root purposes.
Barnacle Tether, Open Garden WiFi Tether.. Turns your phone into a wifi hotspot, for free. F U Verizon.
Volume+.. The external speaker on the GNex is currently lacking, quiet as a mouse even until they update the OS. This app allows you to boost the volume so you wont miss any calls.
Here's an app that doesn't require root access and is available on the market yet verizon has blocked.
Google Wallet.. Turn your phone into a credit card. Pretty funny when I check out at a store and hold my phone up to the credit card swiper and it completes the transaction lol The cashier is like, "huh? I think I need a manager..." haha.
Non rooted apps:
Adobe Flash 11.1
All recipies
Amazon and Amazon App store
Beautiful Widgets. This app is simply Awesome!!!!!!!!!!! Custom clocks and weather are simply stunning.
Big Oven
Brightest Flashlight
Convert Pad - unit converter
Craigs list
Dictonary
Documents to go
Dolphin Browser HD
Drop Box
Easy Money
Ebay
Epicurious
Facebook
GenPlusDroid Sega genesis emulator
Google Reader Rss reader
Google sky map
Google+
IMDB
Kitchen Timer
Knife Steel Compositions
Listen- pod cast app
MapMyRUN+
Google Music- cloud app that you can upload at least 20,000 songs to and access anywhere saving internal memory space
Netflix
Out of Milk- awesome shopping list and memo app
Pandora
PowerAMP- internal music app with eq customization
Poynt- location based yellow/white pages. great for finding businesses, restaurants, theaters etc
Pulse- awesome magazine style rss reader. Combine your favorite web pages here to quickly view articles across the web.
Recipies
Espn ScoreCenter
ScoreMobile
Skype
Speed Test
Tango- video chat cross platform with Iphone users
Google Translate
Twitter
Wikipedia
Xfinity Mobile if you have comcast cable
HBO Go if you have HBO that is
Phew, long list! And that doesn't even cover my favorite games and live wallpapers! Maybe I'll add those later. Enjoy your new phone and have fun app hunting. If you have any questions feel free to ask.