Only games to show of the screen quality and performance is dead trigger, shadow gun, the dark knight and amazing spider man games (those last 2 are pricey though!) etc.
For me, my must have apps are:
file management - airdroid, estrongs
browser - quick ics browser or xscope
games - granny smith, dead trigger, where's my perry, where's my water, sprinkle, N64 and gensoid ROM emulators
video/audio players - BS player (stream films and TV episodes via LAN and can play youtube 720P/1080P back smoothly, can't do this in the browser and youtube doesn't play back true 720P quality since the screen res. isn't 720P) and stock music player for music stored on the phone and google music for cloud storage, TV catchup for live TV
Entertainment/news - flipboard, IMDB
keyboard - either swiftkey or
this
launcher/widgets - apex or nova, snowstorm for weather, APW and smooth calendar for agenda/calendar widgets, switchpro, minimalistic text
camera apps - barcode scanner, google goggles
PC control - unified remote and aWaremote for winamp control
Security and GPS tracker for phone - cerberus
Other nice apps, but not essential are exdialer, oi safe, whatsapp, soundhound, google translate
Everything else like SMS, gallery and camera etc. I just use stock sense apps.