Here are five free iPhone apps that I use all the time. Click the links to get more info via the Apple iTunes Store.

Christian Boyce's Top Five FREE iPhone Apps
NYTimes (Best app for news, reviewed by me here)
Mint (Best app for keeping track of your credit card and bank balances, reviewed by me here)
eReader (Best app for reading books, many of them free, reviewed by me here)
Rimshot & Crickets (Best app for doing "ba-doom-boom, kishhhh" after you say something funny)
BigOven (Best app for recipes)

This list does not include any of the very excellent set of standard iPhone apps (Maps, Mail, Calendar, etc.). I use those apps all the time too.