Some common ones I use quite a bit:
Weatherbug - Weather
Adobe Reader - Read all those PDF's that get attached to emails
RealCalc - Scientific Calculator
Note Everything - Keep notes, shopping lists, etc.
Shazam - Song identifier for those songs you just gotta have
Pandora - Internet radio
IheartRadio - Even better internet radio IMO
ConvertPad - Convert just about any value
Ultrachron Lite - Stopwatch
Droidlight - Flashlight
Astro File Manager - Sorta like a file explorer for your phone storage
Netflix - Watch movies if you subscribe
Karls Mortgage Calculator - Loan calculator
Y5 Battery Saver - Manages wifi to only turn on in places you've ID'd you want it on, ie. home/work
Youtube - Uhh, obvious
GPS Status - GPS app for lat/long, speed, g's, quality, etc.
PdaNet - Tether your phone to your laptop, make a hotspot, etc.
QRDroid - Scan all those QR codes everyones using now
Scanner Radio - Listen to the Police/Fire scanners
QuickOffice - Works with MS Word, Excel, and Powerpoint files
JeepForum - Only if you've got a Jeep...