My ten NON-ROOT apps (in no particular order):
1. Beautiful Widgets
* self-explanatory
2. Clipboard Monitor
* stores things I type a lot (e.g., email addresses)
* let's me copy to clipboard with one tap
* runs in notification area so I can get to it from anywhere
3. Quick Settings
* runs in notification area so I can get to it from anywhere
* allows me to change system settings (wifi, gps, etc.)
* saves me from having to go to Home screen to change settings
4. Tasker
* basically, allows you to program just about anything you want
* just read for yourself:
Tasker for Android
5. Android Agenda Widget
* just about the nicest looking widget I've seen
* shows an agenda of all your calendars in one widget
6. Messaging Widget
* nice-looking SMS reader widget
7. Pure Messenger Widget
* nice but sometimes quirky widget for viewing all kinds of messages
* gmail, email, facebook, twitter, sms ...
* (I use it for gmail and email only)
8. Handcent SMS
* the best SMS client on Android, hands down
9. TuneWiki
* excellent media player with some pretty cool features
* the synced lyrics feature alone is phenomenal
10. FTP Server
* let's me transfer files to/from my PC over wifi, no USB cable necessary