Social
Facebook for Android – Official Facebook application
FourSquare for Android – Official application for Four Square
Media
Winamp for Android – Excellent media player with Wifi sync (if you can get it going)
Last.fm – The official Last.fm Android app, which Winamp for Android can work with too to scrobble your music.
System Utilities
Smart Bar – Application manager, task manager, but I mostly use it for the Quick Settings applet which lets you toggle on and off a lot of the most useful settings: WiFi, GPS, Mobile Data, Auto Refresh etc.
3G Watchdog – Use to monitor your 3G data usage.
AppBrain App Market – Very popular alternative market to the official Android Market
Security
Prey – Help to protect and recover your phone if it’s stolen.
Misc
Astrid Task – To-do list manager
Opera Mobile – Opera’s mobile web browser for smart phones (not to be confused with the not as full-featured Opera Mini).
Google Search with Voice Actions
RunKeeper – Track all information for your running. Pro version free for January 2010.