I've recently gotten myself an Android phone. The Android app market is not as mature as iPhone's App Store, but there is a lot of applications, and plenty of chaff to separate the wheat from. I found most of the apps I use by browsing "top Android apps" lists on the web, so I am putting up a similar list here in case someone finds it useful.
- Everyday apps
- Astrid Task/Todo List - a great To-Do list app that integrates with Remember The Milk
- Quick Calendar - an "upcoming events" widget
- CardioTrainer - nice jogging app, records routes using GPS, integrates with music player
- Language tools
- Thesaurus Free - a thesaurus
- Free Dictionary Org - reference dictionary
- QuickDic German Dictionary - an English-German-English dictionary
- Media content
- Listen - an app to find audio content online
- Mother TED - search and view TED talks
- TuneWiki - music, song lyrics
- Games
- Lumbricidae - guide a worm using your accelerometer
- Flying High - plane flying (also accelerometer-based)
- miniMatcher - memory game
- Iconic Memory - another memory game
- Cool apps
- Phonalyzr - pretty phone call (and SMS) stats
- Shazam - identify a song by recording a short snippet; possibly one of the coolest apps available
- SnapTell - look up product information by scanning a barcode (or even by snapping a photo!)
- Backgrounds - background images
- Google Sky Map - shows constellations
- Layar Reality Browser 3.0 - a fancy-looking Augmented Reality app
- Music
- Sonorox - tune composition for everyone (the pentatonic scale is great, isn't it?)
- Loops! Lite - another music composition app
- Tuner - gStrings - a guitar tuner
- Miscellaneous
- Task Manager - a process monitor utility, useful for checking up on app resource usage
- Currency - a currency converter
- Sleep Logger - a very simple, but useful app for tracking your sleep habits
