I second Cozi.
It's a calendar, to do list, shopping list, etc... that can be accessed from a computer or a smartphone and updates in real time (hubby can be home and put ice cream on the shopping list while you're at the store... so you know to get ice cream)
I also second Gas Buddy
You do not have to log in or have an account, it will just find the closest gas prices to where you are. Just note when that gas price was update! ;-)
I also have twitter, email, facebook and google+ on my phone (but now often forget to check them... which is a good thing with my addictive personality)
I use Zedge for wallpaper, ringtones and notification sounds (though you sometimes have to be creative in your use of search words to find what you're looking for). You can also access Zedge via a computer to search for the ringtones, which saves on battery life (while it's running it's a battery hog, but once you've applied the ringtone/notification sound it's not..)
Also have netflicks (my new addiction), which requires a service plan (but you can access from a computer, internet enabled tv (via Wii, Xbox, Playstation, etc)... so if you have a netflicks account, it's a good app for your phone (I can watch two 40-ish minute tv shows on one battery charge)
Having a Kindle, I have the kindle app, and it will sync books with my kindle reader.
Fandango. If you go to the movies a lot, you can set "favorite" theaters. That way I don't have to wade through all the theater listings to find my fav's to see what's playing when! ;-)
I find I check IMDB enough to have finally downloaded the app!
I have Pandora, but don't use it because I'm usually on my iPod! ;-)
But we used Pandora when we traveled cross-country two years ago, and it was awesome!
I have also downloaded ColorNote. It's like a little postit note for your phone. I used the notes feature on my older (non-smart) phone a lot, so this was very helpful for me.
Most banks have smartphone apps, if you're so inclined.
My husband and I both use Latitude... so I can just check to see where he is (and vice versa). I don't often use it though...
If you have HBO via your cable setup, you can also download HBO GO. (This and Netflix are handy for keeping the kids entertained when they're done, bored and fidgety!)
And finally, a silly one (and not useful until next year). If you're in a girl scout council that sells cookies made by Little Brownie Bakers (you'll know if your Girl Scouts were selling Dulce de Leche, Savannah Smiles or Thank You Berry Much cookies)... Little Brownie Bakers has a "cookie finder" app. When Girl Scout cookie booth sales are happening, you can access the app to find where a booth sale is going on near you. [We downloaded it when traveling, because we wanted to try the aforementioned cookies, and our council doesn't sell them... so we downloaded the app while out of town, found a booth sale and bought some!]
ETA: I also have Accuweather, and check it multiple times every day (first thing in the morning, when my daughter asks if it's going to rain!!!). It has a "hourly" feature so you can see when it is expected to be hottest or rain or whatnot!