It depends on what you want/like - there is really is an app for almost anything - need to read an MRI, find a cab in a strange city, identify that strange bird in yonder tree, learn a foreign language, stay on your Weight Watchers plan, process credit cards, train your dog, find out the phase of the moon on a given date, or learn Morse Code . . . there's an app for each of those.
My faves (all free - a very good price)
WhiteNoise from TMSoft (there is a paid version with more features) - lets you block out surrounding noise with ambient sounds like surf, thunderstorm, crickets, pure white noise, et cetera . . .
Enjoy Sudoku Daily - one game at each of the seven levels each day
Sudoku 101 - in addition to the learning basics option - you can play unlimited games at both the easy and the moderate levels
Same - a very simple but addictive game
AreaCodes - ever gotten a call from a number you didn't recognized and wondered where they were calling from? This app will help you find where the Area Code is from.
myStarbucks - store locator (when connected to wi-fi) and drink customizer - also contains info on different coffee beans they sell by the pound as well as different food products
Kindle for iPhone/iPod Touch - read Kindle books from Amazon on your iPod and when connected to wi-fi, you can shop the Amazon Kindle store for new titles and download them.
Stanza - read a wide variety of books, a lot of them available as free since they tend to be older titles that are in the public domain i.e. the classic works by great authors one is often required to read in high school and college.
Balance - helps you keep track of what's in your bank account.
Declaration of Independence and US Constitution - two different free apps that not only gives one the text of these two vital documents, but biographical info about the singers of the Declaration and a list of proposed amendments that were not ratified in the Constitution app. [Ben Franklin was postmaster of Philadelphia in 1737 and in the late 1970's there was a movement to treat DC like a state - it passed Congress, but failed to be ratified by 3/4ths of the states before the 1985 deadline.]
Drinks Free - mostly alcoholic drink recipes, but there are some non-alcoholic ones too.
Urbanspoon - as seen on the Apple TV adverts - it helps you pick a restaurant [works when connected to wi-fi]
Planets - so what's the best time to spot Mars? This is the app that will tell you the answer. The globe feature is really cool too.
Stars - helps you find the constellations
And my favorite radio station out of Houston (I've never lived there, but I've listed online for years) now has an app - "89.3KSBJ"
Oh and if you ever find yourself in a Sunday school class doing "sword drills" the Holy Bible app is a very useful app to have - much quicker than thumbing through a hard copy trying to remember the order of the minor prophets so you can be the first to find Obadiah.