Beautiful Widgets (cool for big clock and weather forecast widgets)
SwiftKey-X (very cool predictive keyboard)
Google Voice (for voicemail if nothing else, though it can do a lot more, and it's free)
Google Navigator (best navigator I've found and it's free)
Google Translate (very accurate translation app, also free)
Google goggles (pretty cool app which can search by pictures taken from the camera, also it can read barcodes and QR codes.)
Office Suite (great for viewing MS-Office files, and even doing minor edits.)
Kindle (this app works just like a real Kindle, and you can even view books you have on a real kindle, or you can buy them directly to your phone.)
Netflix (awesome if you have a Netflix account)
TweetDeck (great Twitter and Facebook app rolled into one.)
Slacker Radio (streaming radio, I have the paid version and I use it all the time)
System Panel (good for seeing which apps are running and force-stopping them if necessary)
Widgets are awesome, and like s.m.knipe said earlier they go on your desktop screens and offer valuable information right away without having to open an app.
Here is an example.
The big white clock and date and weather at the top of my screen is one of many widgets that come with Beautiful Widgets. Also even this widget can be skinned to look however you want pretty easily.
And if I click on the weather icon it will open up a 5-day forecast.
And if I click the date it will open the calendar.
And if I click the clock it will open my alarm clock settings.