My essential apps are:
Handcent sms - love its ability to interrupt a screen, even the lock screen if desired.
Waze - great social sat nav that can only get better
Swiftkey - wouldn't know how to handle the default keyboard now
Bt SmartTalk - only came across this yesterday but its brilliant. If you have a bt line then you can use this to make your calls over wifi or 3g and it uses the home line plan, mine is all standard calls free. Applied even if using it abroad - obviously data charges apply if applicable. But I'm even using it at home for convenience
Falcon Pro - good twitter app, particularly good at handling certain people like children if you want to quickly see their activity
Bacon Reader - reditt app, i wasn't into reditt but this is getting me into it
Kingsoft Office - use this for my office docs
Lol chat - good league of Legends chat client
Lol memento - good lol champ info
Zeebox - tv schedules
Bus times - uk bus times
Rail tracker
Games - word feud and hexagon