mattstratton says: These are the apps that I figure every single iPhone user needs to have installed. I've tried to generalize somewhat, as my "essentials" may not match everyone's, but I assume 90% of iPhone users will need these apps.
Facebook Kind of goes without saying, but almost anyone who does anything online these days needs access to Facebook. The official app is pretty robust, although it does come with some annoyances.
Twitter I actually kind of dig the official Twitter app (I was a fan of Tweetie 2, which is what this is). Does a lot of what you need out of a Twitter app, and for most users, it will be more than enough.
Adobe Photoshop Express There are a lot of apps for improving the photos taken by your iPhone. I like PS Express for simple adjustments, such as brightness or contrast.
Instagram Want to make your iPhone camera pictures look cool? This app is for you. Period.