The Kindle by Amazon app is really good for getting to read 2 or 3 chapters of books as a sample, to see if you might want to reserve them at the library or buy them.
Stanza is great for lots of free reading (similar to Kindle) but mostly classic books, from what I've found.
Ping! Lite is a way to get free text messaging if your friends with iPhones will also download it.
the Facebook app is free and I love the way it works. The MySpace app doesn't work nearly as well, in my opinion, not even close.
LEGO Photo is fun. It changes photos that you take with your phone into a LEGO format.
The Weather Channel app gives way more info that the built-in weather app, and is free.
MapQuest has a free app, complete with maps and directions, very cool for use as a Navigation system.
Audiobooks Free gives you FREE audiobooks. I found that there are tons of great ones for kids, too. Very cool.
Words with Friends FREE is wonderful, though it sometimes crashes and you have to reload it with a new email address if you have too many games loaded, or for unknown reasons. I still love it and play it all day long, myself.
Jungle Gems and Gemmed Lite are so fun, too. Chain Rxn is great, too.
I even have PacMan LITE. My children have fun with all of them on occasion.
Local Books is a neat app for finding local events at bookstores and libraries that you might want to go to.
For news, there is HuffPost, NY Times, msnbc.com, NPR news, Maddow, AP Mobile, CBC Radio.
For recipes, I love All Recipes, Simply Organic, Epicurious, Whole Foods.
Tip Calculator FREE is neat if you have trouble splitting bills at restaurants or just want to quickly calculate your tip.
Flixster is great for checking out local movies available. IMDb and fandango are also pretty good. Redbox is kind of neat.
WEBMd is kind of neat and might come in handy one day.

Pandora, Rhapsody, Shazam, Last.fm are ways to get free music to listen to.
NFB is the National Film Board of Canada, if you want to watch movies on your device.
Yelp and Around Me! are neat ways to find stuff in your area (restaurants and more)
Take me to my car and Park 'n Find are great when you park in very large parking lots, at amusement parks, zoos and/or malls, etc.
Mint.com is great if you use Mint.
You can probably download an app for your bank account, if you feel comfy doing that.
Tips & Tricks free taught me some very cool things about my iPhone, so much so that I ended up paying the 99 cents for the larger version, but the free version is a great start.
HTH