Dophin HD
Gmail
Jefit
Moon+ Reader
iHeart Radio
Pandora
Dropbox
Google Drive
DeskSMS(if you have paid for/have use for it ... i personally love it)
Phandroid
SMS Backup/Restor (I personally love this)
Steam (again if applicable)
Voice
Wallet (if allowed)
WeatherBug
XDA
YAAIC
Also, if you're on stock ICS, the stock browser is the fastest browser you can get. The only other browser worth trying is Chrome, IMO. But the stock browser is my preference due to its buttery smooth scrolling/zooming even with image intensive sites.
Oh, and AirDroid. Pretty much allows you do anything that you can do on your phone on your desktop (wirelessly); send SMS/MMS, file transfers, change settings, view phone stats, etc. It's amazing and free.
Seekdroid / Where's My Droid, set it and forget it. It saved me from buying a new phone. Fell off my car (I left it on the roof on accident) a half mile away from my house.
Titanium Backup if you root, along with Superuser
LogMeIn
DI radio
Solitaire Free
Bartender
Boat Browser mini
Tethering software of your choice
Flashlight
GasBuddy
SNESoid / Snex9X EX
Netflix
TitaniumBackup
Opera Mini (I think I've tried all the big browsers. This is by far the best overall)
Pulse
Spotify (app is free, Spotify is free, but there is a fee to use it on a phone/tablet etc)
Winamp
Evernote
Groupme
SMS Backup & Restore