I use several of these apps to run my business, like Mint, Evernote and Dropbox, and some of the others I plan to look into a little more deeply. One not mentioned that I highly recommend is Freshbooks. I've used the Freshbooks web app for a couple of years and had to recently move to their paid version (because of adding more clients - a good thing for sure). I particularly like the Freshbooks iPad app. It is very well done and makes keeping track of invoices, expenses and time spent on specific client projects a breeze.
At any rate, take a look at the infographic from Desk.com and let me know your thoughts in the comments. Do you think you could run your small business exclusively through using mobile apps?