A few must have apps for me are:
FileBrowser - browse files over the network (I then airplay videos etc)
iTeleport - VNC App to control my Mac/PC from my iPad anywhere in the World
PhotoSync - Sync photos anyway from Mac-PC-iPhone-iPad (used daily!!)
Facebook - Obvious (Needs retina update though!)
Twitter - Obvious
Remote - Control iTunes and my Apple TV
Spotfy - Sadly only an iPhone app
iPlayer - great cause it supports AirPlay!
Skype - Obvious
Dropbox - I store a lot of files on Dropbox
Deliveries - Track my parcels and things
Brother Print/Scan - Scan from my Brother Printer
WeatherChannel - Check the weather!
MobileMouse - Use my iPad as a trackpad from my couch!
Flipboard - Great way to read headlines from various sites
Engadget - Good tech app
TempleRun - awesome game

hope it helps.