Apps:
- Advanced Task Killer - Close unwanted apps that maybe running in the background.
- Aldiko - eBook reader. Comes with a bunch of free books.
- Astrid Tasks - Best task list manager I have found so far. Has options for tasks list and reminders.
- ASTRO - Best file manager for the phone and SD card.
- AudioManager - Has a widget to control all the audio options for the phone in one place. Must have app if you put your phone on silence / vibrate only / custom audio profile for alerts and notifications.
- Foursquare - App to publish your location information based on nearby establishments. Pushes the same info to Facebook and Twitter.
- Google Sky Map - Shows off a real-time view of the stars based on where you point the phone. Best app to show off to your friends with the "WOW" factor.
- Meebo IM - All in one mobile instant messenger with AIM, Yahoo, MSN, GTalk. But uses a lot of battery if used continuously.
- Mint - All in one money manager to track expenses etc.
- Network - I use it to turn off the GSM radio and use CDMA only. This trick has improved my battery life.
- Photoshop.com Mobile - Have some fun with the pictures taken with the phone. Must have to show off to your iPhone fanboys.
- ShootMe - Phone screenshot grabber.
- Shopper - Google shopping app which has a built in barcode scanner. Runs a Google product search using pictures or barcode.
- Ustream - Live video broadcast phone to their website.
- XKCD Viewer - View XKCD cartoons and the hover over text.
EDIT - added more to the list based on suggestions:
- Dolphin HD Browser - Added to the list since it is faster and more option packed than default browser.
- Compass - Neat app to show off the built in capability.
- ScoreMobile FC - Something to keep track of the World Cup 2010 going on right now.
- World Newspapers
- MITBBS by Chenio Software