(This was in response to somebody asking for Android app recommendations, but it was too long for an LJ comment, and I figured other people would be interested too. This includes Free, free, and for-pay proprietary apps; the links will tell you which is which.)
- B&N Nook
Lets you read Nook books purchased from Barnes and Noble on your phone (also free ebooks in ePub format, such as you can get from Project Gutenberg).
- SlideIT Keyboard
A predictive, sliding keyboard similar to (but not quite as good as the Swype keyboard that’s bundled with some Android phones.
This lets you use your desktop keyboard to type on your Android phone. It works by running a web server on the phone which you can connect to from your desktop web browser, so it requires your desktop computer to be able to reach your phone over the network. (That’ll almost certainly be the case if your phone is on the same WiFi network as your computer, but might not be if your phone is on WiFi and your desktop is on wired Ethernet, and may or may not be depending on your carrier if your phone is using your cellular data network rather than WiFi.)
- 3D Level
Uses the accelerometer on your phone to turn it into a carpenter’s level.
- Adobe Reader
PDF viewer. How usable this will be depends largely on the screen size and resolution of your phone.
- AK Notepad
Handy little note-taking app with cloud integration with Catch.com; you can use it just on the phone, but you can also set up a Catch.com account and create, view, or edit your notes either on the phone or on the web site with two-way synchronization. I find this very handy.
- Aldiko Premium
An ebook reader. Integrates with some ebook stores (but not B&N or Amazon) and some sources of free ebooks. Has some non-English ebook vendors available.
- Amazon Kindle
Lets you read Kindle books purchased from Amazon on your phone (also free ebooks in ePub format, such as you can get from Project Gutenberg).
A Sudoku game, with some variants available for those for whom ordinary Sudoku is too easy.
- Angry Birds Rio
- Angry Birds Seasons
- Angry Birds
- Barcode Scanner
Lets you scan barcodes to open URLs, add contacts, etc.
Podcast manager. Free trial with a for-pay unlock key. Hugely full-featured.
- BeyondPod Unlock Key
- Camera ZOOM FX
An alternative to the built-in camera. Lets you adjust contrast and exposure and the like after taking a picture, and lets you apply special effects, but I got it because I needed a camera program that wouldn’t click when I took a picture, for taking pictures of performances.
Does what it says on the tin.
- Chrome to Phone
In conjunction with the Chrome to Phone extension for Google Chrome, or the Fox to Phone extension for Firefox (which latter is what I use), this lets you send a page from your desktop browser to your phone.
Nifty little puzzle game
Lets you SSH to a server (like PuTTY on Windows) or open a terminal window to type Linux commands to the Android phone itself.
- Crush The Castle
A trebuchet-launching game, on which I gather Angry Birds was loosely based.
A free ebook reader. Probably the best if you don’t need support for DRM-infected ebooks like those from Amazon or B&N.
- Gem Miner: Dig Deeper
A digging and exploring game, a good time-waster.
- Glow Puzzle
A puzzle game in which you attempt to trace a pattern without retracing your steps.
- Google Sky Map
What’s that bright thing in the sky; is it a star or a planet? [point phone] Oh, it’s Sirius! I wonder if Mars is up? [ask phone; follow arrows.] Well, yes, but it’s behind that building there.
Lets you see what’s using the space on your memory card.
For Linux/Unix geeks, this gives you a user interface to launch scripts you have written on the phone. I use it to synchronize photos and podcasts and backups and the like with my home server.
A Jabber client. (If the only Jabber service you use is Google Talk, you might as well use that, but if you have a Jabber server you use at work, for instance, this is a useful chat client.)
- K-9 Mail
Great email client. The built-in GMail client will probably be better if you use GMail, but for other accounts this is probably the best.
Watch movies and TV episodes on your phone. (Or just manage your queue.)
- NPR News
Nothing you can’t get via the web, but the app is convenient and presents things formatted for your phone.
- OI File Manager
Alternative to the Gallery app. Lets you hide particular folders so the Gallery app won’t show them (and so that you have to tap “Show Hidden”, and optionally enter a password, to show them in QuickPic itself). I have no idea what anybody would use that feature for; maybe if you have a photo of confidential legal documents or something? But anyway, it works.
Also for Linux/Unix geeks, this lets you start an SSH server on your phone, and SSH into it to type commands.
- Replica Island
Nifty little open-source running-and-jumping game.
- ROM Manager Premium License
Depending on your phone, if you want to install an alternate ROM (like CyanogenMod), ROM Manager might be the easiest way to do it.
What I used (along with hand-editing the HTML to add these notes) to generate this list.
Fun little platform puzzle game with a twist. Port of an original in Flash that’s playable on the web.
- SMS Backup+
Lets you sync your incoming and outgoing SMS messages to Gmail, so you have a backup. I used this, for instance, to restore my old SMS messages when I switched phones.
This is the Solitaire game whose UI I find easiest to use.
- Speedx 3D
Fun, fast-paced obstacle-avoidance game. Optionally supports Red-Green 3D glasses.
- Unicode Map
Lets you display (and copy and paste) all the characters your phone supports. Useful if you just absolutely have to have a way to get a heart symbol into an SMS, or box-drawing characters into email.
- Where's My Droid
Tool for making your phone ring and/or having it tell you where it thinks it is if you’ve lost it.
Takes photos or video with an interesting special effect; makes things look a bit like a line drawing.
Generated by ShareMyApps (but with comments added by hand)