These are mostly free, a few are $1-2. I find the best apps by just looking at the Top 25 in the Apps Store. They have Top 25 lists for both free and paid apps.

9-toolbox
Don't like the GUI [graphic user interface, for the uninitiated] but it has currency converter, tip calculator, unit converter, ovulation calendar, and a bunch of other stuff. I just got this last night but I can see using this a lot.

ArmyKnife
Kinda like 9-toolbox, has a "flashlight," level, heart rate monitor, unit converter, measuring tape, etc.

Pocket Aid
Has basic guide for all sorts of emergency scenarios.

FML
F My Life for iPhone

SpeakEasy
Records sound and then you can turn it into a file on your computer, which you can edit or whatever.

Urbanspoon
Restaurant finder

Dictionary
A good free dictionary and thesaurus, with audio pronunciation guide.

Doodlejump
Silly fun game with a cool GUI

Good for kids:
Fluide
When you touch the screen, it makes ripples in some water.

iChalky
Animated stick figure that you can manipulate and customize with someone's picture.