Google Sky is totally way cool - use with Compass by Catch.com to calibrate first.
I also like Google Translate for languages and GDocs to access office documents stored in the Google cloud.
Google Gesture Search is just too cool to describe - draw letters on your screen to search your contacts, phone, etc.
Google Earth - I like to armchair travel the deep trenches of the Pacific, I really do.
RealCalc by Overspill - incredibly handy scientific calculator with a full suite of conversions built in.
And - Aldiko, my ebook reader. Couple that with
Project Gutenberg for a host of free books, and
instructions here to use with Aldiko. Works of Shakespeare, Phillip K. Dick's nearly lost works and much, much more - all there for the asking. (I like the goldenrod background with black letter - very easy on the eyes, ok.)
Round it out with WikiMobile and Dictionary.com and you've got an a full research and information tool on your hands.
Finally - for the coolest answers to every question - check out ChaCha Droid - use it to see what I mean. Like Google search for facts - only the answers come from actual humans.
(edit - ask it a fun question and you'll get a fun response)
And, of course, keep your Google Maps up to date - nothing like satellite close-ups of your neighborhood.
tv.com for those free episodes of the original Star Trek.
World Newspapers to keep you up to date on what's going on, and where.
Your built-in News app makes a great aggregator - I get news feeds from here and Great Britain.
Congress - keep right up to date on what your congress-critters are doing and how to give them your feedback.
Rotary Dialer to shut up anyone who questions that smart phones are hard to make calls with.
Each and every one, totally free in the Market.
Oh - and Tricorder - don't forget Tricorder.
Push stuff with funny abbreviations - they're actually buttons.
