Narrowing down the list of my most used apps is a huge undertaking! There are apps that I may use intensively for long periods of time, then not use so much at all. What I tried to do was identify the apps there were used on an almost daily basis, even if they were ones that I didn't use for a long period of time each day. This is perhaps best exemplified by my first choice...
There are a long of weather apps out there (in fact, working on reviews of a couple more!) but My-Cast seems to have the perfect mix of ease of use, simplicity, and providing enough information. It has an "iPhone-like feel" to it, in it's layout and presentation. It has intuitive controls to change between (for example) short of verbose forecast. With My-Cast weather, I find I can get a quick, easy to understand forecast, description of severe weather events, and even radar and map displays. I have other apps that I use for more detailed information when needed, but My-Cast is the app that I check on a daily basis to find out what it going on weather wise.
I use a lot of different online storage systems and email accounts. Air Sharing lets me manage them all together. I can see what it in dropbox, and then move it to Box.net. I can check an attachment I have on my exchange email account, and open it up and read it. The versatility of the app is its strongest feature. No, I can edit documents, but I can print them with air print or email them from withing the app. Air Sharing is a great far-reaching document and storage management tool. (This was almost going to be Goodreader, but that requires a separate app for both the iPad and the iPhone, while Air Sharing is a universal binary).
I wanted to choose a game to put in here. I mostly play casual games (think Angry Birds, Where's my Water, Tower Defense, Temple Run, Doodle God, Fruit Ninja, etc), many of which I may get into a "groove" and play for days on end. I ended up choosing Hanging with Friend, by the makers of Words with Friends. Hanging with Friends is a Hangman style game that you play...well...with friends! While I also play Words with Friends, I have found that Hanging with Friends is probably the casual game I check on a regular basis - seeing if my opponent guessed my word, or trying to guess a word myself. While I enjoy Words with Friends, I find that Hanging with Friends is a little more low key - I don't spend as much time trying to figure out the perfect word to play. It's a great and fun way to play a word game that might be a little less stressful (for me at least!)
I have both the iPhone and the iPad version on the app, and during the baseball season I was using these on a daily basis. As a huge baseball fan, I loved the local radio broadcast feature, and following the game live with Gameday was almost as good as watching it on TV. Even in the off season, I have found that the app gets checked on a regular basis - for news, transaction updates, and anything that might be going on during the Hot Stove season. Unfortunately you have to purchase the app each season, AND they don't make a universal binary, but for any baseball fan it is a must have. And the good news is that each year it has been released, it has had new and improved features, so I hope to see even more improvements in 2012!
Yes, I use Twitter (and Tweetbot is my go-to app). Yes, I use Google+, and use the app for that. But Facebook is the "social network" that I probably check, and make updates too, most frequently. As such, the Facebook app for the iPhone is the app that gets the most use. And now with the Facebook app for the iPad available, I will probably start using that one as well. This may change in 2012, I may start using Twitter or Google+ more, but for now, for me, Facebook is still the king (although I do sometime use Quick Status to update both my Twitter and Facebook accounts at the same time!).