Is it Android?
The ones I have of note would include:
Aldiko for reading books (mainly as a backup if I'm stuck standing in line or something. I have a Nook for my primary reading.)
Astro file manager. Makes it easier to access and manipulate files and folders.
Audible because I subscribe to Audible.com. Great for audiobooks.
Barcode scanner, comes in handy for price comparisons, reading those square boxes of code, etc.
Color Flashlight. Handy when you need a light.
Dropbox, which you load on your phone and home computer. A good way of moving or accessing files between devices.
Fandango for movie times and purchasing tickets.
Google News. For news.
GasBuddy, which gives you gasoline prices in your area. Entered by other people who noticed the prices and entered them, so you know how recent they are. Pretty handy.
Google Sky Map. You know, for stars. (Reads your phone's location and orientation, so when you hold it up, it shows you the sky you're looking at. With labels.)
Lookout. This is very nice. It's like a virus scanner for apps. When you download them it scans them for malicious code.
Netflix. For watching streamed shows from Netflix. Would only use this in wi-fi mode.
Pocket Agent. (State Farm insurance app. Good for recording an accident, holding policy info, etc.)
Slacker. Internet radio. You search for an artist and it will play music from that and similar artists. Or classic rock. Or whatever else you like.
Springpad. For jotting down notes and photos. Can also be accessed from desktop.
Tune-In Radio. Neat app that allows you to access actual over-the-air radio stations from all over the world. There's one in Glasgow that I like.
Yelp. To find local businesses and services that people have rated and to give my own ratings. This has done me a huge amount of good in finding reliable services for things from plumbing to HVAC repair to tile-laying to yard care to restaurants. Very nice.
Anyway, I have more but the ones above have been the most consistently useful. I also have an app for my bank (Chase) and my brokerage/401(k) acct (Charles Schwab.)
Good luck.
