Okay, this thread helped me so here's my list of everyday apps:
Gmail - hey, it just works; notifies of me of incoming mail before my computer does!
Apps Organizer - uses labels to sort apps into categories which appear on the home screen like folders
LiveList - great list making app; I use it for groceries, work agendas, recipes, etc
BatteryTime Lite - calculates remaining time for talk, video/audio playback, web surfing, etc.
My Verizon - for keeping track of my wireless bill and usage
Mint - financial app, syncs with online Mint account where you can create custom budget and watch other finances
Color Flashlight - useful at night; also fun effects
Draw! - makes for a fun time in social situations
craigslistnotifica - keep an eye on specific sections of craigslist; useful notifications and filters
Dictionary.com word of the day - nice widget
Flixster - nice movie app and local theater locater; I like that it's synced with Rotten Tomatoes reviews
Listen - Google's podcatcher
MixZing - best audio/video player, in my opinion; uses internal storage, has video player, Now Playing queue, decent widgets, and other cool features
MyBackup Pro - nightly automatic phone backup to the cloud
Dropbox - allows easy transfer of files between the phone, computers, and the web; free!
