mSecure -- I like being able to conveniently carry around important info in a password-protected package. Also has a desktop version (Mac & Windows) to sync with.
Urbanspoon -- handy when you have no idea where to go for dinner. I found an awesome Cuban restaurant with this app.
The Comixology/Marvel/DC Comics apps are remarkably good on the small iPhone/iPod screen.
Captain's Log -- simply because I'm a dork, and I can flick the phone and it makes the classic communicator noise.
Dicenomicon -- for the sheer nerdiness
Cat Physics -- Throw a ball at a cat!
Aqueduct -- Embrace your inner plumber.
Trainyard -- Traffic management...with trains!
X-Plane -- awesome flight sim ... even though I keep crashing my planes.
Rock Band -- makes my thumbs hurt
Guitar Hero -- not as good as Rock Band, imho. I have problems with it crashing on my 3G phone, but it may run better (hopefully!) on a new iPod Touch.