I recently downloaded Amazon’s Kindle app and am enjoying it. Works best if your screen is large and you don’t have trouble reading small type.
There’s an app called Bathroom Finder that lets you look for and upload the location of public restrooms, which occasionally comes in handy.
Flashlight is very useful. Turns your phone into a low-powered flashlight.
Movies lets you look up showtimes by the movie or the theater, and finds theaters close to you, among other features. (Ratings, previews, buying tickets online, etc.)
If you’re an NPR listener, they have a pretty good app called NPR News. It has stories available for reading or listening, plus the ability to stream most NPR stations.
My fiance and I use an app called Our Groceries for shopping. We both downloaded it and set up a linked account so if one person it at the store, the other person can add something from home and it will instantly appear on the list.
Parkdroid uses GPS to help you remember where you parked. I would use it more if my GPS were more reliable; lately, it’s had trouble figuring out where I am.
I don’t use Shazam much, but it’s really cool: want to know what the name of that song you’re hearing is? Let Shazam listen to it for several seconds and it’ll tell you.
Weatherbug is a better weather app than the one that comes pre-installed; likewise, Better Alarm is, in fact, better than the default alarm clock (it lets you set songs from your library as the alarm sound).
If you’re an XKCD fan, there’s an XKCD Viewer app that shows you the latest comic, lets you browse past comics, tag favorites, send them to friends, post them on Facebook, etc. (And yes, it includes the mouse-over text: just tap the screen on the comic.)