There are few apps that are specific to digital nomads. A few ones that I have seen recommended are:
Trail Wallet - an app that helps you track your expenses across multiple currencies and locations: it looks very useful if you are traveling on a budget.
Tripit - an app that takes your flight and accommodation bookings and generates itineraries how to get from where you are to where you need to be.
Every Time Zone - this is a web app that displays lots of time zones on one page. It may come in handy when you need to schedule things with people who are in different locations.
Apart from these, here are some apps I have used and liked (even though they're not necessarily digital nomad specific):
Toggl - a time tracker that just works. Track how much time you spend on each project.
Wunderlist - a very simple TODO list that lets you keep tasks in folders, set deadlines and create reminders.
F.lux - software that changes the display color of your device depending on the time of the day (and taking your time zone into account).
Workflowy - great noting software that works in terms of lists, and which I mostly use as a web app.
Pocket - a tool for bookmarking articles so you can read them later. It's also worth subscribing to their digests, which include the most bookmarked articles from across the web.
Of course, these are just some of the apps that digital nomads might find useful. There are also plenty of digital nomad websites and other resources available, and, ultimately, everyone has to find their one set of tools that work for them.