"What is the one application I use every day?"
Choosing a single application on a Windows Mobile Device is a very hard task to do since I use many applications throughout the day. The general nature of using a Windows Mobile Device is its multiplicity and ability to run several applications beyond the basic programs for PIM (Personal Information Management)installed by the manufacturer. I will give you a brief description of the ones I use the most on my Windows Mobile devices(Pocket PC and Smartphone).
If I had to choose one, Ilium's eWallet is probably the most valuable one I use to manage my multitude of accounts, passwords, install codes, and other personable data on my PC, Windows Mobile 6 Professional(pocket pc phone edition) and Windows Mobile 6 Standard(Smartphone. It just makes everything easy to use and access all my important information, which is safely encrypted and can only be accessed by a secure password. It can even be installed on U3 USB key for storage and use on any PC with a USB port.
I am also use a huge Sirius Satellite Radio and XM Radio user and like being able to listen to my favorite shows and channels where ever I go. At the several locations where I work it is almost impossible to get a satellite signal for either XM or Sirius, but if you are able to use a third party application like Sirius WM5 (soon to be Sirius GTX)-(this will even run on your old WM2003 device you may have in your drawer great for the house, bathroom, office, etc) or XstreamXM, have a cell phone or wifi data connection, and you are in business listening to satellite radio for free if you are a Sirius or XM subscriber.
Also if you wish to listen to music on your Windows Mobile Device via your bluetooth headset there is a free application called BTAudio and works on both Pocket PC/Professional and Smartphone/Standard devices. The advantage of this is that you don't need a stereo headset with AD2P profile to do this. This is good so you have one free ear to listen to your surroundings, people, can answer phone calls when needed, and use less processing power, thus saving on battery life. The downside is that the audio quality is not as good as A2DP.
Another third party app that is high on my install list is Spb Mobile Shell on my Pocket PC/Windows Mobile Professional. Try it out and you will see why that it adds a lot of functionality that should be there.
The last program I am going to mention that I do use everyday for many functions to place phone calls, show contacts, read my calendar, read incoming titles of new email, manage my music collection on my storage card, launch applications and many other tasks is Microsoft's Voice Command 1.6 which is now included in several ROMS on Windows Mobile 6 devices. If not you can still install it to your device.
Hope this gives you an idea that is hard to pin down just one application, when there are so many to choose from. Each person is different and may use a different program given a particular task at hand. Just make sure you have an adequate toolbox of software to help get you through your day!