These are some of my fav iPhone apps!

Can't live without...
Grocery IQ - I was using my notes, but this is much cooler!
Facebook - for me to stay in touch with all my friends. (and them with me)
Checks Please - great for tips and dividing up checks

Uniqueness...
Ocarina - wins hands down. Who doesn't want to play the flute on their iPhone!!
UrbanSpoon - I use it, but I usually don't use the restaurants it selects; but it gets me thinking outside of my usuals
LIghtsaber - for all you Star Wars fans
iSteam - is cool to look at, but really doesn't do much

Kid Friendly...
Mini Piano - great way to pass time with kids in the car.
Kids Math Fun - a favorite of my 6 year old granddaughter
Labyrinth LE - when the ball hits the wall, actually sounds like it is hitting wood. Very Cool.
DizzyBeeFree - maze like. This is the free version. (Most of my apps are free versions)

Games...
Bejeweled2 - need I say more
Enjoy Sudoku Daily - totally addicted
TapTap Revenge - for all those DDR fans out there. (Your fingers will get a workout with this)

Weather... (I am a weather addict)
Weather Underground - favorite all around; does animated radar and multiple locations
WeatherBug - good current temps page; map allows you to move it around (can move more east/west/north/south)
Accuweather - does animated radar
The Weather Channel - can do multiple locations; temps hourly/36 hour/10 day
(yes, I have 5 weather apps on my iphone - all on the front page)