I have these on the Motorola Droid:
Pandora
Backgrounds
Coin Flip
Compass
Congress - gotta keep track of what my scumbag representative is doing
Currency Converter - Helpful when calculating Euros and Pounds
Discovery - Discovery channel website with cool videos
Documents To Go
Droid Light - turns phone into flashlight
Google Earth
Fishin 2 Go
Full Metal Jacket Soundboard
Funny Jokes
GDocs - UI for Google Documents. I use this for work
Google Translate
Handcent SMS - This is a must have. It replaces the crappy SMS program that comes with your phone
Iheartradio
K-9 Mail - Better than the default e-mail program that comes with your phone
Layar - It is sweet!
Mabilo Wallpapers
Mahjong
Metal Detector
Music Trivia
Opera Mini
Paper Toss
P@yPal
Photobucket
Safe Neighborhood - Lists all sex offenders and gives you a pic and what their offenses are
Scanner Radio
Shazam - Active it and it tells you what song is playing on the radio
Shop Savvy - Barcode scanner/price comparison
SpeedTest
SportsTap
Startup Cleaner
StopWatch
Sudoku Free
Tapatalk - Good for browsing forums. Unfortunately, this site doesn't work
Task Manager
The Hangover Soundboard
Tip Calc
TMZ
TweetCaster
Uninstaller
Unit Converter
Urbanspoon
Voice Recorder
Where
WiFinder
WikiMobile
Wizard Memo
Word Search