Here is a short list of my top 6 apps and how I use them to better run my business. All of them are inexpensive, simple, and best in class.
A simple tool that allows you to "clip" articles from web pages and put them into a single location for reading later (even offline.) Best of all this app syncs across your phone, laptop, tablet and desktop computers so you always have your best content to read. It also takes the articles content out of the annoying and distracting ads and visual noise on the web, and feeds it to you in a clean view.
The perfect place to keep all your notes and reminders. After a meeting I snap a picture of my notes and store it in Evernote. When traveling on business I snap a picture of my receipt and tag it by "receipt" and the trip I'm on. When reading my email, if I know I'll need to find an email for something important it covers, I save it to Evernote (there is a simple plug-in that makes it possible for me to do this with the click of one button). It does all of this and more, flawlessly syncing across devices. I have set up a simple tagging structure that lets me easily find what I need exactly when I need it. This is the best tool I've found to help me manage infoload.
I used to spend a lot of rental cars when traveling on business. Now I just take an Uber. Not only do I get clean cars and incredible drivers, but their app makes ordering and paying for the ride exceptionally intuitive.
I used to have my assistant cut and paste my itinerary for my plane, hotel, and meeting notes into my outlook calendar, but now all she needs to do is forward my itineraries to TripIt and the app organizes my travel for me. The "pro" version even tracks my flights and sends me alerts if they are behind schedule. Absolutely love it. Let's face it, travel sucks, but TripIt takes some of the sting out of it.
Big clock (by Asteria)
The "Big Clock" is just that -- a simple, clean clock that I disables the screen sleep and just shows the clock. I paid 99 cents for it and use it every time I give a keynote. Sometimes the best apps are the most stunningly simple.
Not really an app I know, but I'm a big believer in turning travel or exercise time into learning time, and podcasts are a great way to do this. I have 7 or 8 of them I listen to fanatically and find them a healthy mini-learning feast.